Write an equation of the line (in slope - intercept form) that passes through (-2, 5) and (1, -1).

Answer 1

Slope-Intercept Form

(y-y1) = m(x-x1) where m is slope

m = (y2-y1)/(x2-x1) = (5 - (-1))/(-2 - 1) = 6/(-3) = -2

Therefore slope is -2 = m

Pick either point.

Option 1: (y-5) = -2(x+2)

Option 2: (y+1) = -2(x-1)

you can verify both are correct by converting both to y=mx+b form and see they are the same: y = -2x+1

Answer 2

So Slope Intercept Form takes the form y=mx + b, where m is the slope and b is the y-intercept.

First, we need to know the slope. We can find it using the rise-over-run equation:

(y1-y2)/(x1-x2)=m

Plugging in our two points, we find m=(5 - (-1))/(-2 - 1) = (6)/(-3) = -2

Now that we know m = -2, we can substitute this into our equation:

y = -2x + b

To solve this equation for b, we need to substitute values for x and y. Fortunately, we are given two points on this line, so we can use either (-2, 5) or (1, -1)

Using (1, -1), we get:

-1 = -2 (1) + b

-1 = -2 + b

1 =b.

Thus we have b =1. Our final equation takes the form y = -2 x + 1