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 \((0, -6)\) (the y - intercept) and another point, say \((8, -8)\) (we can also choose other points, but let's use these two for calculation).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 6)\) and \((x_2,y_2)=(8, - 8)\). Then \(m=\frac{-8-(-6)}{8 - 0}=\frac{-8 + 6}{8}=\frac{-2}{8}=-\frac{1}{4}\).

Step3: Use 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 \(m=-\frac{1}{4}\) and from the point \((0,-6)\), the y - intercept \(b=-6\). So the equation of the line is \(y=-\frac{1}{4}x-6\).

Answer:

\(y = -\frac{1}{4}x - 6\)