Question

problem 4c: write an equation of the line.

Explanation:

Step1: Identify two points

From the graph, we can see the line passes through \((0, 10)\) (y - intercept) and \((20, 0)\) (x - intercept).

Step2: Calculate the slope

The slope \(m\) is calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, 10)\) and \((x_2,y_2)=(20, 0)\). Then \(m=\frac{0 - 10}{20 - 0}=\frac{- 10}{20}=-\frac{1}{2}\).

Step3: Use 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 \(m =-\frac{1}{2}\) and \(b = 10\) (from the point \((0,10)\)). So the equation of the line is \(y=-\frac{1}{2}x + 10\).

Answer:

\(y =-\frac{1}{2}x+10\)