Formulas,Applications, Variation

Question

The weekly pay that Kiara receives varies directly with the number of hours she works. If she works 21 hours she makes 329.07. How much money would she make if she works 40 hours?

Answer 1

A direct variation has the form:

y = kx

where k is a constant.

Note that this is equivalent to a linear function, which has the form

y = mx + b

with b=0 and m=k.

In this case, y = pay, k = pay rate, and x = the number of hours. So if pay = $329.07 for 21 hours,

$329.07 = 21 hours × k

Dividing both sides of this equation by 21 per hour,

k = $15.67 per hour

Now that we know the pay rate k, we can use the value of k and this equation to find out how much money Kiara would make if she worked 40 hours:

Pay = y = k × x = $15.67 per hour × 40 hours = $626.80.

In summary, a direct variation equation is simply a special case of linear function equations with b=0 and m referred to as k to emphasize the fact that the slope is constant.