Question

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

Explanation:

Step1: Find two points on the line

The line passes through points $(0, - 2)$ and $(2,0)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(x_1,y_1)=(0,-2)$ and $(x_2,y_2)=(2,0)$, we have $m=\frac{0 - (-2)}{2-0}=\frac{2}{2}=1$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - coordinate of the point where the line crosses the y - axis. From the point $(0,-2)$, $b=-2$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y = mx + b$. Substituting $m = 1$ and $b=-2$, we get $y=x - 2$.

Answer:

$y=x - 2$