Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

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

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1) = (-8, 0)\) and \((x_2, y_2) = (0, -8)\). Then:
\[
m = \frac{-8 - 0}{0 - (-8)} = \frac{-8}{8} = -1
\]

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

The y-intercept is the point where the line crosses the y-axis. From the point \((0, -8)\), we can see that \(b = -8\).

Step4: Write the equation in slope-intercept form

The slope-intercept form of a line is \(y = mx + b\). Substituting \(m = -1\) and \(b = -8\), we get:
\[
y = -x - 8
\]

Answer:

\(y = -x - 8\)