Example 1: Joe is paid an hourly wage. One week he worked 43 hours
and was paid $795.50. How much does he earn per hour?
We can set this up as an equation.
Let y = the total amount of money he earns
Let x = the number of hours he works
Let k = his hourly rate
Then we have:
We can plug in our numbers and find his hourly rate.
Once you figure out his rate, you can figure out how much money he
earns if you are given the number of hours he works. We say that these
two quantities are “directly proportional” or that they “vary directly”.
Section 3.3 – L1 – Page 1 of 7
Here is the equation:
We will discuss three types of variation:
❑
Direct Variation
❑
Inverse Variation
❑
Joint Variation
Section 3.3 – L1 – Page 2 of 7
Direct Variation
For two quantities x and y, if there is a
constant k such that
y = kx ,
We say “y varies directly as x” or
“y is directly proportional to x” or
“y is proportional to x”.
Section 3.3 – L1 – Page 3 of 7
Example 2: P varies directly as t. If t = 6, then P = 120. Express the
statement as a formula. Use the given information to find the constant of
proportionality. (Make sure you restate your formula with the constant
value plugged in!)
Section 3.3 – L1 – Page 4 of 7
Example 3: R varies directly as the square of s. If R = 75, then s = 5.
Express the statement as a formula. Use the given information to find the
constant of proportionality. (Make sure you restate your formula with the
constant value plugged in!)
Section 3.3 – L1 – Page 5 of 7
Example 4: A varies directly as the cube of B. If B = 2, then A = 40.
(a) Write a formula to express the situation.
(b) Find the constant of proportionality.
(c) Find the value of A when B = 1.
Section 3.3 – L1 – Page 6 of 7
Example 5: Hookes’s Law for an elastic spring states that the distance a
spring stretches varies directly as the force applied. If a force of 15
pounds stretches a certain spring 8 inches, how much will a force of 30
pounds stretch the spring?
Section 3.3 – L1 – Page 7 of 7