Question

Paulina’s income from a job that pays her a fixed amount per hour is shown in the graph. Use the graph to find the total income earned for working four 8-hour days all at the standard rate.

Answer 1

Solution

We need to find the equation of an income y at any time x

Using two-point formula

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

At points (1, 10) and (6, 60)

$\begin{gathered} \Rightarrow\frac{y-10}{x-1}=\frac{60-10}{6-1}=\frac{50}{5}=10 \\ \\ \Rightarrow\frac{y-10}{x-1}=10 \\ \\ \Rightarrow y-10=10x-10 \\ \\ \Rightarrow y=10x \end{gathered}$

Four 8 hours = 8 + 8 + 8 + 8 = 32

At x = 32 => y = 10 × 32 = 320

Therefore, the total income for working four 8 hours is $320