Question

determine the equation of the line. (type an equation. simplify your answer. type your answer in slope - intercept form.)

Explanation:

Step1: Find two points on the line

Let's take two clear - cut points on the line. From the graph, we can take $(0, - 8)$ and $(2,4)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0, - 8)$ and $(x_2,y_2)=(2,4)$ into the formula, we get $m=\frac{4-(-8)}{2 - 0}=\frac{4 + 8}{2}=\frac{12}{2}=6$.

Step3: Find the y - intercept $b$

The slope - intercept form of a line is $y=mx + b$. We know that when $x = 0$, $y=-8$. In the equation $y=mx + b$, when $x = 0$, $y=b$. So $b=-8$.

Step4: Write the equation of the line

Substitute $m = 6$ and $b=-8$ into $y=mx + b$. The equation of the line is $y = 6x-8$.

Answer:

$y = 6x-8$