Question

which equation accurately models the graph below:

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-5, 10)\) and \((0, -5)\) (the y - intercept).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-5,10)\) and \((x_2,y_2)=(0, - 5)\). Then \(m=\frac{-5 - 10}{0-(-5)}=\frac{-15}{5}=- 3\).

Step3: Use the slope - intercept form (\(y = mx + b\))

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-3\) and from the point \((0,-5)\), the y - intercept \(b = - 5\). So the equation of the line is \(y=-3x - 5\).

Answer:

\(y = - 3x-5\)