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 $(0, -6)$, so $b = -6$.

Step2: Calculate slope using two points

Use points $(0, -6)$ and $(6, -4)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-4 - (-6)}{6 - 0}=\frac{2}{6}=\frac{1}{3}$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{3}$ and $b=-6$.
$y=\frac{1}{3}x - 6$

Answer:

$y=\frac{1}{3}x - 6$