Question

write the equation of this line in slope - intercept form.

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -4)$, so $b = -4$.

Step2: Calculate slope

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

Step3: Plug into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-\frac{1}{2}$ and $b=-4$.
$y = -\frac{1}{2}x - 4$

Answer:

$y = -\frac{1}{2}x - 4$