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 take the y - intercept $(0, - 2)$ and another point, say $(1,-3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substituting $x_1 = 0,y_1=-2,x_2 = 1,y_2=-3$ into the formula:
$m=\frac{-3-(-2)}{1 - 0}=\frac{-3 + 2}{1}=\frac{-1}{1}=-1$

Step4: Write the equation

Substitute $m=-1$ and $b = - 2$ into the slope - intercept form $y=mx + b$.
We get $y=-x-2$.

Answer:

$y=-x - 2$