Question

the points (-5, 6) and (-1, 9) fall on a particular line. 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 formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-5,6)$ and $(x_2,y_2)=(-1,9)$:
$m=\frac{9-6}{-1-(-5)}=\frac{3}{4}$

Step2: Apply point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use the point $(-5,6)$:
$y-6=\frac{3}{4}(x-(-5))$
Simplify the sign inside the parentheses:
$y-6=\frac{3}{4}(x+5)$

(Alternatively, using the point $(-1,9)$: $y-9=\frac{3}{4}(x+1)$ is also valid)

Answer:

$y-6=\frac{3}{4}(x+5)$ (or $y-9=\frac{3}{4}(x+1)$)