Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -7)$, so $b = -7$.

Step2: Calculate slope

Pick two points: $(0, -7)$ and $(6, -9)$. Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-9 - (-7)}{6 - 0}=\frac{-2}{6}=-\frac{1}{3}$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{1}{3}$ and $b=-7$.

Answer:

$y = -\frac{1}{3}x - 7$