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 the points \((0, 10)\) (the y - intercept) and \((5, 0)\) (the x - intercept).

Step2: Calculate the slope \(m\)

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Using \((x_1,y_1)=(0, 10)\) and \((x_2,y_2)=(5, 0)\), we have \(m=\frac{0 - 10}{5 - 0}=\frac{- 10}{5}=- 2\).

Step3: Use 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 \(m=-2\) and from the point \((0, 10)\), the y - intercept \(b = 10\).
Substituting \(m=-2\) and \(b = 10\) into the slope - intercept form, we get \(y=-2x + 10\).

Answer:

\(y=-2x + 10\)