Chapter 5.2, Problem 28P

Tell whether the two quantities vary directly. Explain your reasoning.

Janine gets paid $ 16.75 per hour at her job. Write a direct variation equation where $h$ represents the number of hours she works and $d$ represents the amount of money she earns. Graph the equation.

To determine

To Write: The equation for direct variation. Also, graph the equation.

Answer to Problem 28P

Yes! The amount earns directly varies with the number of hours worked. The equation is $d=16.75h$ .

Explanation of Solution

Given information: Janine gets paid $16.75 per hour at her job. She works for ‘ h’ number of hours and she earns as‘ d’ .

Calculation:

Let she works for 1 hour, she earns $16.75

If she works for 2 hours, she earns $16.75*2$ Which is $33.5

If she works for 3 hours, she earns $16.75*3$ which is $50.25

So, multiply the number of hours with 16.75 to get the earnings.

The equation is for earning‘ d’ when she works for ‘ h’ hours is

  $d=16.75h$

Hence she earns only variable pay for the number of hours working and there is no fixed pay for the work it gives direct variation equation.

Let’s find two points on the graph and then represent them on the xy plane and join those two points and extend the graph and so on.

Make xy table for some random h values in this context the h values are positive numbers.

x	Y
0	0
1	16.50

Represent (0,0) and (1,16.50) to make graph.

  

In the graph x axis represents the variable ‘ h’ and y axis represents the variable d . It is a straight line starts at origin and increasing and so on for positive values of x.