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: Find two points on the line

From the graph, we can take two points \((0, - 7)\) and \((8,-2)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \((x_1,y_1)=(0,-7)\) and \((x_2,y_2)=(8,-2)\) into the formula:
\(m=\frac{-2-(-7)}{8 - 0}=\frac{-2 + 7}{8}=\frac{5}{8}\)

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

The \(y\)-intercept is the \(y\)-value when \(x = 0\). From the point \((0,-7)\), we have \(b=-7\)

Step4: Write the equation in slope - intercept form \(y=mx + b\)

Substituting \(m = \frac{5}{8}\) and \(b=-7\) into the formula:
\(y=\frac{5}{8}x-7\)

Answer:

\(y=\frac{5}{8}x - 7\)