Question

How do you write the equation of the line that passes through the points (-9,4) and (7,-2)

Answer 1

y = (-3/8)x + 5/8

Explanation:

First we need to find the slope of the line connecting these two points. Slope is represented by m and is equal to rise/run.

Going from the first point to the second, we see x increasing by 16 (this is the run) and y decreasing by 6 (this is the rise). Thus, the slope of this line is

m = rise/run= -6/16, or -3/8.

Adapt the slope-intercept formula y = mx + b to this situation. From the point (-9, 4) we get x = -9 and y = 4, and m = -3/8. Then we have:

4 = (-3/8)(-9) + b, from which we get the y-intercept, b:

4 = 27/8 + b, or 32 = 27 + 8b, or 8b = 5, so that b = 5/8.

The equation describing this situation is y = (-3/8)x + 5/8.

Answer 2

y = -3/8x+5/8.

Explanation:

First, we'll find the slope. This is (y_2-y_1)/(x_2-x_1). So, we do -2 - 4 / 7 --9. This goes to -6/16. Simplifying gets us -3/8. Now, we have y= -3/8x + b. We can solve for b by plugging in points. Using the first point, it goes to 4 = 27/8+b, we can solve for b now, getting us 5/8. So, the complete equation is y = -3/8x+5/8.