Question

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 \((0, -8)\) (the y-intercept) and \((6, 1)\).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -8)\) and \((6, 1)\):
\(m = \frac{1 - (-8)}{6 - 0} = \frac{9}{6} = \frac{3}{2}\)

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

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, -8)\), we can see that \(b = -8\).

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

Substituting \(m = \frac{3}{2}\) and \(b = -8\) into the formula:
\(y = \frac{3}{2}x - 8\)

Answer:

\(y = \frac{3}{2}x - 8\)