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Problem 52 Hard Difficulty

Find an expression for the function whose graph is the given curve.

The line segment joining the points $ (-5 , 10) $ and $ (7 , -10) $


$y=\frac{-5}{3} x-\frac{25}{3}+10$

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Video Transcript

Okay. We want to find the equation of the line that goes through these two points. Actually, we just want the segment. Okay, so we need the slope and we need the y intercept. So to find the slope, we're going to use the slope formula. Why? To minus y one, which would be negative. 10 minus 10 over x two minus x 17 minus negative five. And that gives us negative. 20/12. We can reduce that to negative 5/3. So the slope of the line is negative. 5/3. Now we can find the y intercept, and we can use point slope form to help us. So point slope form is why minus y one equals m times X minus X one. We can substitute either one of our points in for X one y one. So I'm going to use the 1st 1 So I have y minus 10 equals negative 5/3 times a quantity X minus, negative five. And let's simplify that. First of all, X minus negative five is the same as X plus five. Now we can distribute the negative 5/3. So if y minus 10 equals negative 5/3 X, minus 25 3rd and then we'll attend to both sides and adding 10 is the same as adding 33rd. So when we had 33rd to negative 25 3rd we get 5/3. So this is the equation of the line that goes through those two points and because we just want the segment, we can restrict the domain and we can just have it started negative five and end at seven.