Question

this graph shows how the total number of comic books cole has in his collection is related to the amount of money he spends on additional comic books. how much money does cole need to spend on additional comic books in order to have a total of 90 comic books in his collection?

Explanation:

Step1: Find the slope of the line

The line passes through the points \((0,60)\) and \((400,100)\).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{100 - 60}{400-0}=\frac{40}{400}=\frac{1}{10}\)

Step2: Write the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(0,60)\) and \(m = \frac{1}{10}\), the equation is \(y=60+\frac{1}{10}x\)

Step3: Solve for \(x\) when \(y = 90\)

Substitute \(y = 90\) into \(y=60+\frac{1}{10}x\)
\(90=60+\frac{1}{10}x\)
Subtract \(60\) from both sides: \(90 - 60=\frac{1}{10}x\)
\(30=\frac{1}{10}x\)
Multiply both sides by \(10\): \(x = 300\)

Answer:

\(300\)