Problem

Use either the slope-intercept form (from Section…

03:24

Problem 67 Hard Difficulty

Use either the slope-intercept form (from Section 3.5) or the point-slope form (from Section 3.6) to find an equation of each line. Write each result in slope-intercept form, if possible.
Passes through $(-2,-1)$ and $(-1,-5)$

Answer

$$y=-4 x-9$$

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 write the equation of a line that passes through the points. Negative too negative one and negative one negative five. Well, whenever rewrite the equation of a lime, the first thing we need is our slow. What? We can do this using our slow formula, which is m equals Y sub two minus. Why someone over, except to minus sechs someone. So I'm gonna go back and label my ordered pairs. My first ordered pair is going to be labeled X of one. Why someone And then the 2nd 1 repair will be, except to why sub too. And we simply need to substitute these values into the formula. So we're gonna have m equals. Why sub two, which is negative five minus weiss of one, which is negative one all over, except to which is negative one minus x of one, which is negative too. And now we just need to simplify. Well, negative five minus negative one is negative for and negative one minus negative too is equal to one Well, negative four divided by one. It's just negative for So now we know the soap of our life Well, because we're not given the Y intercept. We have to use point slope form to write this equation. Well, remember, point slope form is why minus y someone equals m times the quantity of X minus except one. And to use this form, we need em, which is to slope, which we've already found to be negative for. And we also need to know, ex of one and why someone which represents a point in our line. Well, remember, we've already labeled our first order pair. That's on our line x of one and Weiss of one so we can use thes values. So now we're gonna substitute these values into the formula. So we're gonna have y minus y someone which is negative. One equals m, which we found to be negative for times to quantity off x minus x of one, which is negative too. Now our directions tell us that our final answer has to be in slope intercept form. In other words, why has to get all by itself? We'll take a look at the left hand side of the equation. We have two negatives right next to each other, which will simply become a positive. So we'll have. Why plus one and then equals negative four times to quantity off. Now, also in that Prem facie, we have two negatives next to each other, which will also become a positive. So we'll have X plus two. Now, on the right hand side of the equation, we need to distribute the negative four to the X Plus two. So we're still gonna have why plus one equals Well, negative Four times X is negative for X and negative. Four times two is negative. Now, to get why by itself, we need to move that one to the other side. Well, to do that, we're going to subtract one from both sides of the equation and we're going to subtract. It's from it's like term of negativity. So on the left hand side, we have one minus one, which is zero. So those caroms cancel out and I'm gonna put my final answer right here in the middle of kind of run that over. So we're gonna have y equals Well, we're gonna bring down that negative for ex term and then negative eight minus one is negative. Nine. So now we're in our final answer and slope intercept form. So our answer is why equals negative for X minus night

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