Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -20)\) (the y - intercept) and \((-4, -8)\).

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 20)\) and \((x_2,y_2)=(-4, - 8)\). Then \(m=\frac{-8-(-20)}{-4 - 0}=\frac{-8 + 20}{-4}=\frac{12}{-4}=-3\).

Step3: Write the equation in 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 \(m=-3\) and from the point \((0,-20)\), \(b=-20\). So the equation of the line is \(y=-3x-20\).

Answer:

\(y = - 3x-20\)