Question

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

Explanation:

Step1: Identify slope-intercept form

Slope-intercept form is $y = mx + b$, where $m$ is slope and $b$ is y-intercept.

Step2: Find y-intercept ($b$)

The line crosses y-axis at $(0, -6)$, so $b = -6$.

Step3: Calculate slope ($m$)

Use two points, e.g., $(-9, 0)$ and $(0, -6)$.
Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 0}{0 - (-9)} = \frac{-6}{9} = -\frac{2}{3}$.

Step4: Write the equation

Substitute $m = -\frac{2}{3}$ and $b = -6$ into $y = mx + b$:
$y = -\frac{2}{3}x - 6$.

Answer:

$y = -\frac{2}{3}x - 6$