Question

a line includes the points (2, 9) and (4, 8). 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 $(x_1,y_1)=(2,9)$ and $(x_2,y_2)=(4,8)$. Then $m=\frac{8 - 9}{4 - 2}=\frac{-1}{2}=-\frac{1}{2}$.

Step2: Write the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(2,9)$ and $m =-\frac{1}{2}$, we get $y - 9=-\frac{1}{2}(x - 2)$.

Answer:

$y - 9=-\frac{1}{2}(x - 2)$