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 \((0, -1)\) and \((3, -3)\).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1) = (0, -1)\) and \((x_2, y_2) = (3, -3)\). Then:
\(m = \frac{-3 - (-1)}{3 - 0} = \frac{-3 + 1}{3} = \frac{-2}{3}\)

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

The slope-intercept form is \(y = mx + b\). We know the line passes through \((0, -1)\), which is the y-intercept (since \(x = 0\) here). So \(b = -1\).

Step4: Write the equation

Substitute \(m = -\frac{2}{3}\) and \(b = -1\) into \(y = mx + b\):
\(y = -\frac{2}{3}x - 1\)

Answer:

\(y = -\frac{2}{3}x - 1\)