Question

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

Explanation:

Step1: Identify intercept and points

The y-intercept $b$ is $-6$ (where the line crosses the y-axis). Choose two points on the line: $(0, -6)$ and $(6, -9)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{-9 - (-6)}{6 - 0}=\frac{-3}{6}=-\frac{1}{2}$

Step3: Write slope-intercept form

Substitute $m=-\frac{1}{2}$ and $b=-6$ into $y=mx+b$.
$y = -\frac{1}{2}x - 6$

Answer:

$y = -\frac{1}{2}x - 6$