Question

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

Explanation:

Step1: Identify intercept and point

The y-intercept $b$ is $-6$ (where the line crosses the y-axis). A clear point on the line is $(5, -9)$.

Step2: Calculate slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(0, -6)$ and $(5, -9)$.
$m=\frac{-9 - (-6)}{5 - 0}=\frac{-3}{5}$

Step3: Plug into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{3}{5}$ and $b=-6$.
$y=-\frac{3}{5}x - 6$

Answer:

$y=-\frac{3}{5}x - 6$