a line passes through the points (-5, 10) and (4, -8). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-5,10)$ and $(x_2,y_2)=(4,-8)$. Then $m=\frac{-8 - 10}{4-(-5)}=\frac{-18}{9}=- 2$.

Step2: Use point - slope form to find the y - intercept

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-5,10)$ and $m = - 2$, we have $y - 10=-2(x+5)$. Expand the right - hand side: $y - 10=-2x-10$.

Step3: Rewrite in slope - intercept form

Add 10 to both sides of the equation $y - 10=-2x-10$. We get $y=-2x$.

Answer:

$y=-2x$