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 \((-8, -1)\) and \((0, -5)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-8, -1)\) and \((x_2,y_2)=(0, -5)\). Then \(m=\frac{-5 - (-1)}{0 - (-8)}=\frac{-5 + 1}{8}=\frac{-4}{8}=-\frac{1}{2}\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0, -5)\), we can see that \(b=-5\).

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

Substitute \(m = -\frac{1}{2}\) and \(b=-5\) into the slope - intercept form. We get \(y=-\frac{1}{2}x-5\).

Answer:

\(y = -\frac{1}{2}x - 5\)