Complete the equation of the line through (-10,3) (-8,-8)

The correct equation is y = [tex] \frac{-11}{2} [/tex]x - 52.

In order to find this, we first must use the slope formula. The slope formula allows us to tell what the m value is for our slope intercept form (y = mx + b).

Slope (m) = [tex] \frac{y1 - y2}{x1 - x2} [/tex]

Slope (m) = [tex] \frac{3 - -8}{-10 - -8} [/tex]

Slope (m) = [tex] \frac{3 + 8}{-10 + 8} [/tex]

Slope (m) = [tex] \frac{11}{-2} [/tex]

Now that we have the slope at [tex] \frac{11}{-2} [/tex], we can use that value and one of the ordered pairs to find the intercept (b), using the equation y = mx + b.\

y = mx + b ---> plug in known values
3 = [tex] \frac{11}{-2} [/tex](-10) + b
3 = [tex] \frac{110}{2} [/tex] + b
3 = 55 + b
-52 = b

Now we can use those two (m and b) to write the equation. 

y = [tex] \frac{11}{-2} [/tex]x - 52