Answer:
y=-8(x+6)
Step-by-step explanation:
The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,
First we are going to calculate m:
If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case we have A=(-5,-8) and B=(-7,8)
[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]
Replacing in the formula:
[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]
Then [tex]y=-8x+b[/tex].
We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:
Replacing the point (-5,-8):
[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]
Or replacing the point (-7,8):
[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]
The answer is the same with both points.
Then we have:
y=-8x-48
y=-8(x+6)
