Question

Find the equation of the line in slope-intercept form that passes through the following points. Simplify your answer.

(−5,−8) and (−7,8)

Answer 1

slope intercept form: y = -8

Answer 2

y=-8(x+6)

Explanation:

The equation of a line is
`y=mx+b` where m is the pending and b is the y intercept,

First we are going to calculate m:

If you have two points
`A=(x_(1),y_(1))\\B=(x_(2),y_(2))`,

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

In this case we have A=(-5,-8) and B=(-7,8)

`x_1=-5, y_1=-8\\x_2=-7,y_2=8`

Replacing in the formula:

`m=(8-(-8))/((-7)-(-5))\\\\m=(16)/(-2) \\\\m=-8`

Then
`y=-8x+b`.

We have to find b, we can find it replacing either of the points in
`y=-8x+b`:

Replacing the point (-5,-8):

`y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b`

Or replacing the point (-7,8):

`y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b`

The answer is the same with both points.

Then we have:

y=-8x-48

y=-8(x+6)