Answer
y=-$\frac{8}{5}$x-$\frac{71}{5}$
Work Step by Step
Slope-intercept form is written as
y=mx+b.
m=$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$, and it's given that $x_{1}$=-7, $x_{2}$=-12, $y_{1}$=-3, $y_{2}$=5, we can solve for m by plugging in the givens into the slope equation.
Therefore, m=$\frac{5-(-3)}{-12-(-7)}$=$\frac{8}{-5}$=-$\frac{8}{5}$.
Now we know that y=(-$\frac{8}{5}$)x+b=-$\frac{8}{5}$x+b, and we can solve for b by plugging in one of the two points, in this case we'll plug in the point (-12,5)
5=(-$\frac{8}{5}$)(-12)+b, so 5=$\frac{96}{5}$+b, and after we subtract $\frac{96}{5}$ from both sides, b=-$\frac{71}{5}$
Therefore, y=-$\frac{8}{5}$x-$\frac{71}{5}$
