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 \((3, - 1)\).

Step2: Calculate the slope \(m\)

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

Step3: Write the equation in slope - intercept form

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 \(m=-1\) and from the point \((0,2)\), we know that \(b = 2\). So the equation of the line is \(y=-x + 2\).

Answer:

\(y=-x + 2\)