Question

find the equation of the line. use exact numbers. for a negative y - intercept, type a negative sign. y = x+

Explanation:

Step1: Find the slope

The line passes through points $(2,0)$ and $(0, - 8)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 2,y_1=0,x_2 = 0,y_2=-8$. So $m=\frac{-8 - 0}{0 - 2}=\frac{-8}{-2}=4$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y=-8$, so $b=-8$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 4$ and $b=-8$ into the equation, we get $y = 4x-8$.

Answer:

$y = 4x-8$