When two proportional relationships are represented in different ways, we compare them by finding a common piece of information.
For example, Clare’s earnings are represented by the equation $y=14.5x$, where $y$ is her earnings in dollars for working $x$ hours.
The table shows some information about Jada’s pay.
Who is paid at a higher rate per hour? How much more does that person have after 20 hours?
||time worked (hours)
In Clare’s equation we see that the constant of proportionality relating her earnings to time worked is 14.50. This means that she earns \$14.50 per hour.
We can calculate Jada’s constant of proportionality by dividing a value in the earnings column by a value in the same row in the time worked column. Using the last row, the constant of proportionality for Jada is 13.25, since $490.25\div37=13.25$. An equation representing Jada’s earnings is $y=13.25x$. This means she earns \$13.25 per hour.
So Clare is paid at a higher rate than Jada. Clare earns \$1.25 more per hour than Jada, which means that after 20 hours of work, she has $20\boldcdot \$1.25 = \$25$ more than Jada.