Question

write the equation of this line in slope-intercept form.

Explanation:

Step1: Identify two points

From the graph, we can see two points on the line: let's take \((-4, 8)\) and \((0, -8)\) (the y - intercept).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(-4,8)\) and \((x_2,y_2)=(0, - 8)\), we have \(m=\frac{-8 - 8}{0-(-4)}=\frac{-16}{4}=-4\).

Step3: Determine the y - intercept \(b\)

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-8)\), we know that \(b=-8\).

Step4: Write the equation in slope - intercept form

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

Answer:

\(y = - 4x-8\)