Question

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

Explanation:

Step1: Identify slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The line crosses the y - axis at $(0,-2)$, so $b=-2$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's use $(0, - 2)$ and $(3,-4)$. The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substitute $x_1 = 0,y_1=-2,x_2 = 3,y_2=-4$ into the formula:
$m=\frac{-4-(-2)}{3 - 0}=\frac{-4 + 2}{3}=\frac{-2}{3}$

Step4: Write the equation

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

Answer:

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