Answer:
[tex]\displaystyle y=\frac{-8}{3}x-3\frac{2}{3}[/tex]
Step-by-step explanation:
Slope-intercept form is y = mx + b. This is where m is the slope and b is the y-intercept.
We will be writing a point-slope equation, then simplifying it into a slope-intercept form equation. First, we need to find the slope. We find that we have a slope of [tex]\frac{-8}{3}[/tex].
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{1-9}{-2--5} =\frac{-8}{3}[/tex]
Next, we will write the point-slope equation.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - 9 = [tex]\frac{-8}{3}[/tex](x - -5)
y - 9 = [tex]\frac{-8}{3}[/tex](x + 5)
y - 9 = [tex]\frac{-8}{3}[/tex]x - 13[tex]\frac{1}{3}[/tex]
y = [tex]\frac{-8}{3}[/tex]x - 3 [tex]\frac{2}{3}[/tex]