Question

a line includes the points (-6, 2) and (10, -10). what is its equation in point - slope form? use one of the specified points in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-6,2)$ and $(x_2,y_2)=(10,-10)$. Then $m=\frac{-10 - 2}{10-(-6)}=\frac{-12}{16}=-\frac{3}{4}$.

Step2: Write the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-6,2)$ and $m =-\frac{3}{4}$, we get $y - 2=-\frac{3}{4}(x+6)$.

Answer:

$y - 2=-\frac{3}{4}(x + 6)$