1 d
Equation of a line that passes through two points?
Follow
11
Equation of a line that passes through two points?
Example 2: Find the equation of the line joining the points (3, 6) and (2, -5). Articles that describe this calculator Equation of a line given two points A linear equation is an equation that represents a line. Suppose we have two points A and B whose position vector is given as [Tex]\vec a[/Tex] and [Tex]\vec b[/Tex]. Mathematical equations are an essential part of many academic and professional disciplines. The following type of question is quite popular with examiners at the institution where I study. Move the sliders below or the points on the graph to their appropriate locations. Substitute the values in the Two-Point formula given by. The function defined by the equation f(x) = mx + b is called a linear function. Calculate the slope from 2 points. Point-slope is the general form y-y₁=m (x-x₁) for linear equations. The formula is slope = (y₂ - y₁)/ (x₂ - x₁), where. Just as a line is determined by two points, a plane is determined by three. Example 2: Find the equation of a line having an x-intercept of 5 units and a y-intercept of 4 units. The line is y - x = 0 or for that matter any circle through the origin given by f(x, y; a, b) = x^2+y^2+2ax+2by=0 If the circle passes though (0, 1) and (1, 0), a = b = -1/2, and the circle is given by x^2+y^2-x-y=0 If the the number of parameters is more than two, two points are not sufficient. 3x + y = 7. How do you write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation?. Solution: The coordinates of the point is (3, 4, 2), and the direction cosines of the perpeThe ndicular vector are 2, -3, 1. In other words, for any two distinct points, there is exactly one line that passes through those points, whether in two dimensions or three. Similarly, given any three points that do not all lie on the same line, there is a unique plane that passes through these points. This is pretty straightforward, since point-slope form requires you to just substitute values in order to form the equation. The points through which the line passes are (2,-4) and (6,10). We can rewrite an equation in point-slope form to be in slope-intercept form y=mx+b, to highlight the same line's slope and y-intercept Oct 6, 2022 · The line y=−4 is a horizontal line. The opposite reciprocal of the equation would be or Plug the point into the slope equation to find the y-intercept. anyways, the standard linear equation is ax+by=c, while the standard quadratic equation is slightly different from what you have; it should be ax^2+bx+c=0. Type the slope m m of the line (numeric expression) =. r = a + K(b − a) r = a + K ( b − a) My question: If we are given 2 points how do we determine which point is to be taken as b and which as a? For example: Here's a question from my book: Find the equation of line passing through A (5, 1, 6), B (3, 4, 1). The angle the line makes with respect to the x-axis (measure anti-clockwise). Example 1 Write down the equation of the line that passes through the points \(\left( {2, - 1,3} \right)\) and \(\left( {1,4, - 3} \right)\). Express the equation in standard form. x – x 1 a = y – y 1 b = z – z 1 c. The slope calculator shows the work and gives these slope solutions: Slope m with two points In this article, we have covered the derivation and the sample problems to find the equation of the straight line passing through the two points. The Equator passes through the Asian country of Indonesia. Try It! Let the given two points be P (x 1, y 1) and Q (x 2, y 2 ). Solution: The given equation of the line is 3x + 5y - 15 = 0. Let a and b be the position vectors of two points A (x 1 y 1 z 1) and vectors of two points B (x 2 y 2 z 2), respectively that are lying on the line. Update: Some offers mentioned below are no longer available. Result: Now you have calculated all three variables (A, B and C) for the General Form Linear Formula. This moment is called t. Download the set Determine the equation of a straight-line that passes through two points (−5;10) and (−3;4) y=3x−5 y=3x+5 y=−3x−5 y=−3x 0. by: Hannah Dearth When we realize we are going to become parents, whether it is a biological child or through adoption, we immediately realize the weight of decisions before we You can now earn 1,000 bonus points just by joining the Sonesta Travel Pass loyalty program. Use to calculate the equation of the line, where represents the slope and represents the y-intercept. A line's slope is a measure of its steepness and direction. The calculator also has the ability to provide step by step solutions. Simplify. The form y=mx+b means slope m and y-intercept b; similarly, the form y=mx+a means slope m and y-intercept a. Any line perpendicular to it must be vertical, in the form x=a. In other words, for any two distinct points, there is exactly one line that passes through those points, whether in two dimensions or three. To sketch the graph of the line, as we've done in Figure \(\PageIndex{6}\), plot the y-intercept at P(0, 3), then move 4 units to the right and 3 units down to the point Q(4, 0). Step 2: Apply the two point formula given as, y−y1 y − y 1 = y2−y1 x2−x1 (x−x1) y 2 − y 1 x 2 − x 1 ( x − x 1). It passes in a uniform direction. Two equations are parallel if they have equal slope. Remember, the slope formula is: m = y2 − y1 x2 − x1. In many cases, especially real-world situations, you are given neither the slope nor the y−intercept. So, to find an equation of a line that is parallel to another, you have to make sure both equations have the same slope. The figure (shown in 2D for simplicity) shows that if P is a point on the line then. And subtract the y value of the other point (the other point is (3,2) so the y value is 2): 6-2=4. If the line passes through two points A(x 1, y 1) and B(x 2, y 2), such that x 1 ≠ x 2 and y 1 ≠ y 2, then equation of line. And there we have it! The equation of a line that passes through the point (2, −1) ( 2, − 1) and is parallel to the line y = 3x + 4 y = 3 x + 4 is y = 3x − 7 y = 3 x − 7. Explanation: First you must figure out what point has an x-intercept of 3. A line in R2 is given by an equation of the form. You can now earn 1,000 bonus points just by joining the Sonesta Travel Pass loyalty program. Answer: Step-by-step explanation: Find the slope of the line first using the slope formula: Substitute the two given points into this formula. Find the negative reciprocal of the slope. Math equations are an integral part of many fields, including mathematics, physics, engineering, and finance. Let a and b be the position vectors of two points A (x 1 y 1 z 1) and vectors of two points B (x 2 y 2 z 2), respectively that are lying on the line. ξx + ηy + ζ = 0, (1) where either ξ and/or η are nonzero. Do this substituting the. Example 4: The equation of a horizontal line that passes through the point (−2,−5) ( − 2, − 5) may be written as follows: y = −5 y = − 5 Its slope is equal to zero because the above equation may be written as : y. Point slope form, this page's topic, makes it easy to find the line's equation when you only. Find the equation of the line passing through the points (2, 3) and the point of intersection of the lines 4 x − 3 y = 7 and 3 x + 4 y + 1 = 0. Let L L be a straight line through 2 + i 2 + i and 3 − 2i 3 − 2 i in the complex plane. So, we have, ax 1 + by 1 = c. It is an archipelago consisting. The cartesian equations of a straight line passing through a fixed point ( x 1, y 1, z 1) having direction ratios proportional to a, b, c is given by. Let L L be a straight line through 2 + i 2 + i and 3 − 2i 3 − 2 i in the complex plane. Find the equation of a line given slope and point step-by-step point-slope-form-calculator Related Symbolab blog posts Nope, this is serious stuff; it's about finding the slope of a line, finding the equation of a line Cooking Calculators. Find the Equation Using Two Points (2,3) , (4,7) , Step 1. Well, there's a few different ways to define a plane. can be found using the following formula Nov 28, 2020 · Writing an Equation Given Two Points. However, creating and formatting complex equations can be a daunting t. Any line can be represented as, ax + by = c. Its formula is given by, y – y1 = m (x – x1) or. From the figure, we can say that the three points P 1, P 2 and P are collinear. Most states impose a sales tax on individual purchases of goods and services. Here's what you need to know Out with the old, and in with the new. It is an archipelago consisting. choose any value for x and find the matching value for y. High School Math Solutions - Perpendicular & Parallel Lines Calculator. The y-intercept of the line. Find the equation of the line in all three forms listed above. A line in R2 is given by an equation of the form. → = → + ( → − →) , for a line passing through two points with position vectors → and → . This equation can also have the form. The two points form is one of those methods. blondelashes porn Have a play with it (move the point, try different slopes): The equation of a line that passes through two points and is perpendicular to each other has slope "5" and ⅕ respectively. Jan 18, 2024 · We will assume you know two points that the straight line goes through. Find the equation of this line in point slope form, slope intercept form, standard form. Learn how to boost your finance career. Your unknowns are the slope m and the y-intercept b. Working on the Equation of a Line Calculator: You can find the equation of the line point-slope form, slope-intercept form and standard form additionally we are able to find the equation of a line with two points on. This online calculator finds parametric equations for a line passing through the given points. Also, express the equation obtained in the slope-intercept form. Once we have the value of c, we can substitute it back into the equation y = mx + c to get the final equation of the perpendicular line. It is an archipelago consisting. ARAM Points are a curren. It's important to keep hydrated before, during, and after a workout, but if you're not satisfied with conventional "until you're not thirsty" wisdom, Men's Health explains how to c. ) The second line will pass through ( −2, 1) ( −2, 1) and have m = 2 To graph the line, we start at ( −2, 1) ( −2, 1) and count out the rise and run. Type in the letter of the equation that is the answer for each question. Equation of the Line in Two-point Form. The picture is the same for 3D. Suppose, for example, we know that a line passes through the points [latex]\left(0,\text{ }1\right)[/latex] and [latex]\left(3,\text{ }2\right)[/latex]. (-3)-(-7)/(-1)-(-2)=-4/-1=4. Find the slope and both the intercepts. spelling bee answers and analysis Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Step 1. Find the equation of the line shown We need to find the slope and y -intercept of the line from the graph so we can substitute the needed values into the slope-intercept form, \ (y=mx+b\). y₁ = the y-coordinate of the first point. We will let this point be 𝑥 sub zero, 𝑦 sub zero, and 𝑧 sub zero. formula: y2-y1 over x2-x1. Determine the slope of the line passing through the points. Let P 1 (x 1, y 1) and P 2 (x 2, y 2) be the two given points on the line L. Remark 2 : The parametric equations of the line x – x 1 a = y – y 1 b. To fix that, we just need to pick any point on our line to. y = =1/2 x + b, so 4 = -1/2 (-2) + b, 4 = 1 + b, b = 3 and your perpendicular equation is. Writing the Equation of a Line Using Two Points. Choose a point that the parallel line will pass through. In total, the equator passes through 12 countries When you want to hit the road for an adventure, a camper is an integral part of the equation. In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. Use the formula to find the slope between the two points. In this we will discuss two cases, when line passes through two points and when. pornmuslim It can also be seen that Δx and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the. Find the Equation Using Two Points. We’ll use the notation m ∥ m ∥ to represent the slope of a line parallel to a line with slope m. What I want to calculate is the midpoint between two locations (latitude and longitude) on a sphere. This is done exactly as shown in Tutorial 15: The Slope of the Line, where m is the slope and b is the y -intercept when the linear equation is written in the form y = mx + b. Equation of the Line: Example 3: Find the equation of a line in a slope-intercept form which passing through the points (-2, 5) and (3, 6). For this, we first need to find the slope of the line. How to Find the Equation of the Line in Space Passing through Two PointsWe find the parametric and symmetric equations of a line in space given two points. ARAM Points are a curren. slope y2−y1 x2−x1 11−75−3 42 = 2 slope y 2 − y 1 x 2 − x 1 11 − 7 5 − 3 4 2 = 2 Substitute the slope for 'm' in the slope intercept form of the equation. Result: Now you have calculated all three variables (A, B and C) for the General Form Linear Formula. Finding the Equation of a Line Given Two Points 2 - Cool Math has free online cool math lessons, cool math games and fun math activities. Y= The location of the point on the Y axis. Therefore, the cross-product of is 0 which is given by: where, d, e, and f are the coefficient of vector equation of line AB i, example 1: Determine the equation of a line passing through the points and. If you ask your kids to manipulate m = (y - k)/(x - h), perhaps one will come up with (y - k) = m(x - h) Another way to think about point-slope form is as a transformation of the canonical line y = mx: That is to say, (y - k) = m(x - h) is the end result of a vertical. It is more challenging, but you can find the equation of the line that would pass through those two points. Find the equation of the line passing through the point of intersection of 2 x. A.
Post Opinion
Like
What Girls & Guys Said
Opinion
22Opinion
It is more challenging, but you can find the equation of the line that would pass through those two points. Let's understand the steps to find the equation of a line using two-point form. We can compute the coefficients of the line y = a*x + b that connects the two points using the polyfit method from numpy import matplotlib # Define the known points. The image of financial services has always been dominated by the frenetic energy of the trading floor, where people dart and weave en masse. Equation of line passing through 2 points with position vectors a a and b b is. Using this formula Examples of Gradient of a Line. The straight line through two points will have an equation in the form \(y = mx + c\). Are you an avid player of Teamfight Tactics (TFT) and want to know how many ARAM points you need to reach different tiers in the TFT Pass? Look no further. Find more worked-out examples in the database of solved problems Equation of a Line: Standard Form - Level 1. x2 would be 11 and x1 would be 9 we divide 6 by 2 and we get a slope of three. Learn how to boost your finance career. Scientists have come up with a new formula to describe the shape of every egg in the world, which will have applications in fields from art and technology to architecture and agric. tukiffes porn Therefore, this is the slope between the points and : m = Change in y Change in x = − − = = 2 . The Ecell equation, also known as the cell potential equation, is a fundamental concept in electrochemistry. The slope of the line A P = y 1 − y 2 x 1 − x 2. 1. Example 2: Find the vector equation of a plane passing through a point (3, 4, 2), and is perpendicular to a line with direction cosines of 2, -3, 1. We can find the midpoint of any two points in three dimensions by. The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Created by Sal Khan and Monterey Institute for Technology and Education. It is denoted by the symbol m. Your unknowns are the slope m and the y-intercept b. It passes in a uniform direction. This online calculator finds equation of a line in parametrical and symmetrical forms given coordinates of two points on the line. Find the equation of the line that passes through the point P(−2, 2) that is parallel to the line passing through the points Q(−3, −1) and R(2, 1) We want to find the equation of the line through these two points, which is the same type of problem we tackled in Example 6. Let P (x, y, z) be another point on the plane. video de porne Let P (x, y) be a general point on the line L. Update: Some offers mentioned below are no longer available. y₁ = the y-coordinate of the first point. Since we are talking about a line in 3-D, it is more appropriate to talk about its direction vector than its slope. Equation of the line passing through two different points on plane. Find the equation of a line given slope and point step-by-step line-given-slope-point-calculator Related Symbolab blog posts. Since we are talking about a line in 3-D, it is more appropriate to talk about its direction vector than its slope. example 3: If points and are lying on a straight line, determine the slope-intercept form of the line. View Solution Q 3 The straight line through two points will have an equation in the form \(y = mx + c\). The cartesian equation of a line is. An example of paralell lines would therefore be: (1) y = mx + b With b and c being any constants. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. The calculator also has the ability to provide step by step solutions. Simplify. It passes in a uniform direction. Substitute the coordinates of your known point P P to find. anal twinks Type the slope m m of the line (numeric expression) =. Since the slope of the line multiplied by -3/2 must equal -1, we can write the following: (slope of the line)(-3/2) = -1. For problems 6 & 7 determine the slope of the line and sketch the graph of the. For this, we first need to find the slope of the line. Step 1: Enter the point and slope that you want to find the equation for into the editor. In order to write the equation of a line in point-slope form, we will need two essential things here which are the slope of the two given points and any point found on the line. Have a play with it (move the point, try different slopes): The equation of a line that passes through two points and is perpendicular to each other has slope "5" and ⅕ respectively. Substituting the first point and the slope gives: (y −1) = 2 3(x − 2) Substituting the second point and the slope gives: (y −3) = 2 3(x − 5) We can solve this for y to put it in the more familiar slope-intercept form: Find an equation of a plane that passes through the point $(0, 1, 0)$ and is parallel to the plane $4x - 3y + 5z = 0$ I first plugged the "missing" variable $4x - 3y + 5z - d = 0$ then calculate. The equation point slope calculator will find an equation in either slope intercept form or point slope form when given a point and a slope. The cartesian form of line is given by using the coordinates of two points located in space from which the line is passing. Trish states that the parallel line is y - 2 = -1 (x - 4). Indonesia is located in Southeastern Asia between the Indian Ocean and the Pacific Ocean. Do they appear perpendicular? The coordinates of a point on this line farthest to the origin and at a distance of 14 units from A is (r) (2, 5, 7) (d) The coordinates of the foot of the perpendicular from the point (3, − 1, 11) on the line x 2 = y − 2 3 = z − 3 4 is/are (s) (14, 1, 5) When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. Solution: Equation of line in two-point form: Substitute and. The Equator passes through the Asian country of Indonesia. Free parallel line calculator - find the equation of a parallel line step-by-step Find the equation of a line given two points step-by-step line-given-points-calculator Related Symbolab blog posts. The first one will have coordinates (x₁, y₁) and the second one (x₂, y₂). The slope of a line through the points (3, 4) and (5, 1) is $$- \frac{3}{2}$$ because every time that the line goes down by 3(the change in y or the rise) the line moves to the right (the run) by 2. Here (x 1, y 1) and (x 2, y 2) are the points on the line. First, use the points (32, 0) and (212, 100) to determine the.
Substituting the two points give in the problem allows us to calculate the slope as: Write an equation of a line given the y intercept and another point. Example 1: Find the equation of a straight line that passes through the points (1, 3) and (-2, 4). The formula to find the gradient of the line is m = y2 −y1 x2 −x1 y 2 − y 1 x 2 − x 1 = 2−4 3−(−5) 2 − 4 3 −. The "point-slope" form of the equation of a straight line is: y − y 1 = m (x − x 1) The equation is useful when we know: one point on the line: (x1, y1) and the slope of the line: m, and want to find other points on the line. Demetri states that the parallel line is y = -x + 6. Worked example: slope from two points About Transcript. Substitute these values into y = m𝑥 + c; Examples of using the Formula for the Equation of a Line Given Two Points. japanese porn films We will assume you know two points that the straight line goes through. Astronomically, spring begins at the precise point in time when the center of the sun passes directly over the Equator. Our goal is to come up with the equation of a line given a vector v parallel to the line and a point (a,b,c) on the line. Find the coordinates of the two points on this line which are at a distance of 5 units from A. The "point-slope" form of the equation of a straight line is: y − y 1 = m (x − x 1) The equation is useful when we know: one point on the line: (x1, y1) and the slope of the line: m, and want to find other points on the line. Enter coordinates of the first and second points, and the. Now put that slope and one point into the "Point-Slope Formula". Where m is the slope and (x1,y1) and (x2,y2) are the two points. replika nude And the way to think about these, these are just three different ways of writing the same equation. You are doing this because at the two lines' point of intersection, both lines will share the same x and y value. Vector equation Vector equation of a line passing though two points with position vectors 𝑎 and 𝑏 is 𝑟 = 𝑎 + 𝜆 ( 𝑏 − 𝑎) Given, Let two points be A (-1, 0, 2) & B(3, 4, Find the standard form equation of a line that passes through the points ( − 6, 1) and (4, 7). If we multiply both sides by -2/3, we will find the slope of the line. Identify the slope: m = 2; Input the values into the point-slope form formula: y − y 1 = m (x − x 1) \small y - y_1 = m (x - x_1) y − y 1 = m (x − x 1 ) 4. Note again that the slope is m = −3/4 and the line slants “downhill. The image of financial services has always been dominated by the frenetic energy of the trading floor, where people dart and weave en masse. hamstrer xxx Slope of a line= Slope of perpendicular line= The equation of a line passing through the point (with slope m is given by. Example 2: Find the equation of a plane into cartesian form, which is passing through the point (2, 3, 4), and is perpendicular to the line having direction ratios as 5, -3, 2. First, identify a vector parallel to the line: ⇀ v = − 3 − 1, 5 − 4, 0 − ( − 2) = − 4, 1, 2. It can also be seen that Δx and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the.
Try It! Let the given two points be P (x 1, y 1) and Q (x 2, y 2 ). Step 1: Enter the point and slope that you want to find the equation for into the editor. Welcome; Videos and Worksheets; Primary; 5-a-day. My assignment was to write an equation of a line that is perpendicular to y = 7/5x + 6, that passes through point (2,-6). Question 2 Find the equation of the line that passes through the point (-2 , 5) and has a slope of -4. That's all you need to express everything we need to know about the plane in order to define it uniquely, but there's a way of. Learn how to boost your finance career. Since the slope of a horizontal line is 0, the general formula for the standard form equation, y = mx + b becomes y = 0x + b y = b. The slope, or steepness, of a line is found by dividing the vertical change (rise) by the horizontal change (run). Similarly, given any three points that do not all lie on the same line, there is a unique plane that passes through these points. This one's a two-stepper How To Write Equation of a Line in Two Point Form. The equator does not pass through the Arctic Ocean and Southern Ocean, or Antarctic Ocean. Determine the slope of the line passing through the points. Slope = (4-3)/ (-2-1) = -1/3. Here r = (x, y, z) is a vector representing any general point on the line. Do this substituting the. Find the Equation Using Two Points. The cartesian equations of a straight line passing through a fixed point ( x 1, y 1, z 1) having direction ratios proportional to a, b, c is given by. hannahowo fucked Every relationship is different, and so is every breakup. 4 - Equation of a Horizontal Line. where k is the parameter. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. If you've been eagerly. example 3: If points and are lying on a straight line, determine the slope-intercept form of the line. You can use this calculator to solve the problems where you need to find the line equation that passes through the two points with given coordinates. Or we could choose another value for x, such as 7: y = 2×7 + 1 = 15. Let L be a line in R3 which has direction vector →d = [a b c]B and goes through the point P0 = (x0, y0, z0). Find the y intercept given two points. The equation point slope calculator will find an equation in either slope intercept form or point slope form when given a point and a slope. This gives you y = 3x + b. ALWAYS! So, what do we do if we are just given two points and no slope? No problem -- we'll just use the two points to pop the slope using this guy: Check it out: Let's find the equation of the line that passes through the points. By clicking "TRY IT", I agree to receive newsletters and promotio. Updated version (2022): https://youtu. A line passes through the points (− 2, − 4) and (− 5, 5) . The function defined by the equation f(x) = mx + b is called a linear function. Use the method for writing an equation from the slope and a point on the line. Ski Vacation? Nope, this is serious stuff; it's about finding the slope of a line, finding the equation of a line. First, identify a vector parallel to the line: ⇀ v = − 3 − 1, 5 − 4, 0 − ( − 2) = − 4, 1, 2. The "point-slope" form of the equation of a straight line is: y − y 1 = m (x − x 1) The equation is useful when we know: one point on the line: (x1, y1) and the slope of the line: m, and want to find other points on the line. To calculate the equation of the line, use the format A line in 50 dimensions would just be a representation of a set of values. literotica com com Besides the parametric form, another equation of a line in 3D to get it in the form f(x, y, z) = 0 could be written as: r − r0 r − r0 ⋅ n = 1. In fact, you can substitute any ordered pair solution of the line to find \(b\). We can determine the equation of a linear function when we have the slope and a y intercept which is a starting point for drawing our line. Let us derive the point slope form of a linear equation mathematically. Therefore, the cross-product of is 0 which is given by: where, d, e, and f are the coefficient of vector equation of line AB i, example 1: Determine the equation of a line passing through the points and. Input two points using numbers, fractions, mixed numbers or decimals. The equation point slope calculator will find an equation in either slope intercept form or point slope form when given a point and a slope. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept There are basically two intercepts, x-intercept and y-intercept. The Equator passes through the Asian country of Indonesia. This equation can be in the standard form (Ax + By + C = 0) or in the slope-intercept form (y = ax + b). (0,0) ( 0, 0) Use the slope-intercept form to find the slope m = 2 m = 2. Learn how to boost your finance career. Use the method for writing an equation from the slope and a point on the line. r = a + K(b − a) r = a + K ( b − a) My question: If we are given 2 points how do we determine which point is to be taken as b and which as a? For example: Here's a question from my book: Find the equation of line passing through A (5, 1, 6), B (3, 4, 1). Let's understand the steps to find the equation of a line using two-point form. My answer was y = -5/7x - 4 4/7 It said that I was incorrect however, so I looked at the hints. is parallel to the given axis. Find the Equation Using Two Points (2,3) , (4,7) , Step 1. Example 1 Write down the equation of the line that passes through the points \(\left( {2, - 1,3} \right)\) and \(\left( {1,4, - 3} \right)\).