Question

a line passes through the points (10, 2) and (-8, -7). 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 $(x_1,y_1)=(10,2)$ and $(x_2,y_2)=(-8,-7)$. Then $m=\frac{-7 - 2}{-8 - 10}=\frac{-9}{-18}=\frac{1}{2}$.

Step2: Write the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(10,2)$ and $m = \frac{1}{2}$, we get $y - 2=\frac{1}{2}(x - 10)$.

Answer:

$y - 2=\frac{1}{2}(x - 10)$