Answer
y=-$\frac{5}{7}$x+$\frac{5}{7}$
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 $x_{1}$=-6, $x_{2}$=1, $y_{1}$=5, $y_{2}$=0, we can solve for m by plugging in the givens into the slope equation.
Therefore, m=$\frac{0-5}{1-(-6)}$=$\frac{-5}{7}$=-$\frac{5}{7}$.
Now we know that y=(-$\frac{5}{7}$)x+b=-$\frac{5}{7}$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 (1,0)
0=(-$\frac{5}{7}$)(1)+b, so 0=-$\frac{5}{7}$+b, and after we add $\frac{5}{7}$ to both sides, b=$\frac{5}{7}$
Therefore, y=-$\frac{5}{7}$x+$\frac{5}{7}$
