Problem

Find an equation of the line that passes through …

02:51

Problem 29 Medium Difficulty

Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible. See Example 2.
Passes through $(1,7)$ and $(-2,1)$

Answer

$$y=2 x+5$$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 6

Point–Slope Form

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Video Transcript

we're being asked to use point Slope form to write an equation that passes through the two points 17 and negative to one. Well, remember point slow form is the equation. Why, minus wise up one equals m times the quantity of X minus X sub one. And the first piece of information we need is a slope. While we're not given the soap in this case, however, we are given two points on our line so we can use our so formula, which remember, is M equals Y sub two minus y sub one over except to minus except one. Well, if I go back and label my ordered pairs, my first order pair is ex of one y someone. My second order pair is, except to why sub too. So I simply need to substitute these values into my equation. So I'll have m equals y sub two, which is one minus Weiss of one, which is seven all over, except to which is negative too. Minus X of one which is one. And now we need to simplify. Well, one minus seven is negative. Six negative two minus one is negative. Three and negative six divided by negative three is positive to now we know our slope with just two. Now, we also need a point in our line. That's what ex of one and why So one represents. Well, remember when we found the slope he already labeled except one And why someone the order Pair 17 So we're going to use this point when we go and use our point slope form. So here's what we're gonna have. We're gonna have Why? Minus why someone which we said was seven equals R Slope, which we found to be too times a quantity of X minus. And our except one value is one. Now, our directions tell us to put our final answer and slope intercept form, meaning to get why by itself. To do that, we need to distribute the two on the right hand side of the equation. So we'll be left with y minus seven equals two time sex with just two X and two times negative one, which is negative too. Now, to get why by itself, we need to move the negative seven to the other side. And to do that or simply gonna add seven toe, it's like terms of negative, too. So negative seven plus seven cancel. So we're left with y equals the two X comes down and negative two plus seven is positive. Five. So our final equation is why equals two X plus five.

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