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 the points \((-6, -1)\) and \((0, -7)\) (the y-intercept is at \((0, -7)\)).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1) = (-6, -1)\) and \((x_2, y_2) = (0, -7)\). Then:
\[
m = \frac{-7 - (-1)}{0 - (-6)} = \frac{-7 + 1}{6} = \frac{-6}{6} = -1
\]

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

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

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

Substitute \(m = -1\) and \(b = -7\) into the slope-intercept form:
\[
y = -x - 7
\]

Answer:

\(y = -x - 7\)