Question

the table shows the relationship between the amount of money earned and the time spent working, in hours. write an equation relating the number of hours worked, x, and the total amount earned, y.

time (hr)	5	10	15	20
amount earned ($)	42.50	85	127.50	170

Explanation:

Step1: Find the rate of pay

We know that the relationship between hours worked ($x$) and amount earned ($y$) is a linear relationship of the form $y = mx + b$. In a situation where there is no starting - up amount (i.e., when $x = 0$, $y=0$), the equation simplifies to $y=mx$, where $m$ is the rate of pay. To find $m$, we can use the formula $m=\frac{y}{x}$. Let's take the first pair of values: $x = 5$ and $y = 42.50$. Then $m=\frac{42.50}{5}=8.5$.

Step2: Write the equation

Since $m = 8.5$, the equation relating the number of hours worked $x$ and the total amount earned $y$ is $y=8.5x$.

Answer:

$y = 8.5x$