NAME:_____________________________________________
Algebra 2/Trig – Direct and Inverse Variation CLASSWORK
DATE:_________
PERIOD:_______
 Today we are going to examine the relationship between 2-variables!
DIRECT VARIATION
This is a graph of direct variation.
If the value of x is increased, then y increases as well.
Both variables change in the same manner.
If x decreases, so does the value of y.
We say that y varies directly as the value of x.
Keywords:
Direct Variation Formula:
1. If x varies directly as y and x = 25 when y = 5, find x when y = 20.
2. Keisha earned $44.70 for working 6 hours. How much does she earn, to the nearest cent, for working 8.5
hours?
 Why would this be a direct variation?
INVERSE VARIATION
Notice the shape of the graph of inverse variation.
If the value of x is increased, then y decreases.
If x decreases, the y value increases.
We say that y varies inversely as the value of x.
Keywords:
Inverse Variation Formula:
1. If y is inversely proportional to x and y = 9 when x = 6, find y when x = 3.
2. Carlos drove from his home to Union College in 4 hours at 50 mph. How long would it take him, to the nearest
hour, if he had traveled at 65 mph?
 Why would this be an inverse variation?
MORE DIFFICULT VARIATIONS
1. If y is inversely proportional to the square of x, and y = 4 when x = 6, find y when x = 2.
2. If x varies directly as the square root of y, and x = 5 when y = 49, find x when y = 9.
3. Every year students at West High School collect canned goods for a local food pantry. They plan to distribute
flyers to homes in the community asking for donations. Last year, 12 students were able to distribute 1000 flyers
in five hours. How long would it take 15 students to hand out the same number of flyers this year?

Is this a direct or inverse variation? Why?
PRACTICE
1. The salary in a particular workplace varies directly. If 6 men earn a total of $1260 in a week, what will 4 men,
working at the same rate of pay, earn in a week?
2. The speed of a gear varies inversely as the number of teeth. If a gear which has 30 teeth makes 25 revolutions
per minute, how many revolutions per minute will a gear with 15 teeth make?
3. A map of Illinois is scaled so that 2 inches represents 15 miles. How far apart are Chicago and Rockford if they
are 12 inches apart on the map?
4. If x is inversely proportional to the cubic root of y, and y = 27 when x = 3, find y when x = 2.