Algebra
11.3 Notes
Name:_
Mitchell
11.3 Direct and Inverse Variation
Direct Variation:
The variables x and y vary directly if for a constant k:
.
Example 1: Find an equation that relates x and y such that x and y vary directly, and y = 4 when x = 2.
Step 1, write the direct variation equation:
1:
Step 2, substitute your x and y :
2:
Step 3, solve for k:
3:
Step 4, plug k back into the direct variation equation:
4:
Example 2: x varies directly with y. y = 6 when x = 2. Find the equation that relates x and y.
Example 3: x varies directly with y. x = 3 when y = 12. Find the equation that relates x and y.
Example 4: x varies directly with y. y = 8 when x = 4. What is y when x = 5?
Step 1-4:
Step 5, plug second x in and solve:
Inverse Variation:
The variables x and y vary inversely if for a constant k:
.
Example 5: Find an equation that relates x and y such that x and y vary inversely, and y = 4 when x = 2.
Steps 1-4:
Example 6: x varies inversely with y. y = 6 when x = 2. Find the equation that relates x and y.
Example 7: x varies inversely with y. y = 4 when x = 8. What is y when x = 2?
Steps 1-5:
Example 8: x varies inversely with y. y = 2 when x = 10. What is x when y = 5?
Try the following direct and inverse variation problems
1) y varies directly with x. y=16 when x=2. Write
an equation that relates x and y.
Answer:_______________________________
3) y varies inversely with x. y=3 when x=33.
Write an equation that relates x and y.
Answer:_______________________________
5) y varies directly with x. y=18 when x=8. What
is the value of y when x=2?
Answer:_______________________________
7) y varies directly with x. y=24 when x=8. What
is the value of y when x=64?
Answer:_______________________________
9) The circumference of a circle varies directly
with the radius of the circle. The circumference
equals 69.08 when the radius equals 11. What
is the circumference of a circle that has a radius
of 4?
Answer:_______________________________
2) y varies inversely with x. y=9 when x=4. Write
an equation that relates x and y.
Answer:_______________________________
4) y varies directly with x. y=10 when x=6. Write
an equation that relates x and y.
Answer:_______________________________
6) y varies inversely with x. y=5 when x=7. What
is the value of y when x=21?
Answer:_______________________________
8) y varies inversely with x. y=12 when x=12.
What is the value of y when x=15?
Answer:_______________________________
10) The time that it takes Eric to drive to his
girlfriend’s house varies inversely with the rate
that he travels. If he drives at a rate of 50
mph, it takes him 30 minutes. How long
would it take if he drove 75 mph?
Answer:_______________________________