Complete the equation of the line through (-8,8) and (1,-10).

Answer 1

We know two points: (-8,8) and (1, -10). To complete the equation of the line in slope intercept form, we need the slope, m, and the y-intercept, b.

y = mx+ b

First, we find the slope using rise/run

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

Let’s break our original points into x1, y1, x2, and y2:

-8 = x1

8 = y1

1 = x2

-10 = y2

Plug into the slope equation:

m = (-10 - 8) / (1 - (-8))

m = -18 / 9

m = -2

slope is -2

Next, we will choose either of our starting points (-8,8) or (1,-10)(doesn’t matter which one, you get the same answer) to help us find b, the y intercept. I am going to use the point (1,-10), so I will use:

x = 1

y = -10

m = -2

b = ?

y = mx+b plug in our known values

-10 = (-2)(1) + b multiply -2*1

-10 = -2 + b add 2 to both sides

-8 = b

the y intercept is b = -8

Finally, we put the equation together. x and y will remain as variables but we will put in the values we found for m and b.

y = mx+b

y = -2x - 8

Answer 2

(y-y1) / (x - x1) = (y1-y2) / (x1-x2)

(x1,y1) = (-8, 8)

(x2,y2) = (1, -10)