Question

Question was provided via image upload.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-6, 0)\) and \((0, -4)\).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-6, 0)\) and \((x_2, y_2)=(0, -4)\). Then \(m=\frac{-4 - 0}{0 - (-6)}=\frac{-4}{6}=-\frac{2}{3}\).

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

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, -4)\), we see that \(b=-4\).

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

Substituting \(m = -\frac{2}{3}\) and \(b=-4\) into the slope - intercept form, we get \(y=-\frac{2}{3}x-4\).

Answer:

The equation of the line is \(y = -\frac{2}{3}x-4\)