Question

graph the line that passes through the points (-9, 8) and (-3, 6) and determine the equation of the line.

Explanation:

Step1: Calculate slope of the line

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(-9,8)$ and $(x_2,y_2)=(-3,6)$
$m=\frac{6-8}{-3-(-9)}=\frac{-2}{6}=-\frac{1}{3}$

Step2: Find y-intercept using point-slope

Use $y-y_1=m(x-x_1)$, substitute $m=-\frac{1}{3}$ and $(-3,6)$:
$y-6=-\frac{1}{3}(x-(-3))$
$y-6=-\frac{1}{3}(x+3)$
$y-6=-\frac{1}{3}x -1$
$y=-\frac{1}{3}x +5$

Step3: Verify graph alignment

The line passes through $(-9,8)$ and $(-3,6)$, and crosses the y-axis at $(0,5)$, matching the provided graph.

Answer:

The equation of the line is $\boldsymbol{y=-\frac{1}{3}x + 5}$
(The graph is already correctly plotted with the line passing through $(-9,8)$ and $(-3,6)$, extending in both directions.)