determine the equation of the line.\n(type an equation. simplify your answer. type your answer in slope…

Explanation:

Step1: Find two points on the line

Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$ from the graph. For example, if we take two clear - cut points, say $(0, - 4)$ and $(2,4)$.

Step2: Calculate the slope $m$

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

Step3: Use the slope - intercept form $y=mx + b$

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that when $x = 0$, $y=b$. From the point $(0,-4)$, we can see that $b=-4$.

Step4: Write the equation of the line

Substitute $m = 4$ and $b=-4$ into $y=mx + b$. The equation of the line is $y = 4x-4$.

Answer:

$y = 4x-4$