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 \((0, 1)\) (the y - intercept) and \((5, 0)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, 1)\) and \((x_2,y_2)=(5, 0)\). Then \(m=\frac{0 - 1}{5 - 0}=\frac{- 1}{5}=-\frac{1}{5}\).

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 \(m =-\frac{1}{5}\) and \(b = 1\) (since the line crosses the y - axis at \((0,1)\)). So the equation of the line is \(y=-\frac{1}{5}x + 1\).

Answer:

\(y = -\frac{1}{5}x + 1\)