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 $(0, 6)$, so $b=6$.

Step2: Calculate slope $m$

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

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-3$ and $b=6$.
$y=-3x+6$

Answer:

$y=-3x+6$