complete the equation of the line through (-6,5) and (-3,-3). use exact numbers. y =

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-6,5)$ and $(x_2,y_2)=(-3,-3)$. Then $m=\frac{-3 - 5}{-3-(-6)}=\frac{-8}{3}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-6,5)$ and $m =-\frac{8}{3}$, we have $y - 5=-\frac{8}{3}(x + 6)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y - 5=-\frac{8}{3}x-16$. Add 5 to both sides: $y=-\frac{8}{3}x-11$.

Answer:

$y =-\frac{8}{3}x - 11$