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 $(0, -4)$, so $b = -4$.

Step2: Calculate slope

Use two points, e.g., $(0, -4)$ and $(2, -7)$.
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-7 - (-4)}{2 - 0} = \frac{-3}{2}$

Step3: Write slope-intercept form

Slope-intercept form: $y = mx + b$
Substitute $m = -\frac{3}{2}$ and $b = -4$.

Answer:

$y = -\frac{3}{2}x - 4$