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 \((0, -2)\) (the y-intercept) and \((3, -5)\).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -2)\) and \((3, -5)\):
\(m = \frac{-5 - (-2)}{3 - 0} = \frac{-5 + 2}{3} = \frac{-3}{3} = -1\)

Step3: Write the equation in slope-intercept form (\(y = mx + b\))

The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We know \(m = -1\) and from the point \((0, -2)\), \(b = -2\). So the equation is:
\(y = -1x - 2\) or simplified as \(y = -x - 2\)

Answer:

\(y = -x - 2\)