Algebra I Part 1
Unit 3 Day 7 - Variation
Name: _______________________________
Name the constant of variation for each equation. Then find the slope of the line that passes through each
pair of points.
1.
.
y
6
4
y = 4x
(1, 4)
2
x
-4
(0, 0)2
-2
4
-2
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
2. If y = 6 when x = 10, find x when y = 18.
3. If y = 4¼ when x = ¾, find y when x = 4 ½.
4. TRAVEL A map of North Carolina is scaled so that 3 inches represents 93 miles. How far apart are Raleigh
and Charlotte if they are 1.8 inches apart on the map?
Determine whether each table or equation represents an inverse or a direct variation. Explain.
5.
X Y
1 30
2 15
5 6
6 5
6.
X Y
-4 -2
-2 -1
2 1
4 2
7. 5x – y = 0
8. x = 14y
Assume that y varies inversely as x. Write an inverse variation equation that relates x and y. Then graph the
equation.
9. y = 2 when x = 20
10. y = -6 when x = -3
11. y = -4 when x = 16
Solve. Assume that y varies inversely as x.
12. If y = 12 when x = 3, find x when y = 6.
13. If y = 4 when x = 14, find x when y = -5.
14. If y = 15 when x = -2, find y when x = 3.
15. EARTH SCIENCE The water level in a river varies inversely with air temperature. When the air
temperature was 90° Fahrenheit, the water level was 11 feet. If the air temperature was 110° Fahrenheit,
what was the level of water in the river?
Determine whether each situation is an example of an inverse or a direct variation. Justify your reasoning.
16. The drama club can afford to purchase 10 wigs at $2 each or 5 wigs at $4 each.
17. The Spring family buys several lemonades for $1.50 each.
18. Nicole earns $14 for babysitting 2 hours, and $21 for babysitting 3 hours.
19. Thirty video game tokens are divided evenly among a group of friends.
20. PHYSICAL SCIENCE When two people are balanced on a seesaw, their distances from the center of the
seesaw are inversely proportional to their weights. If a 118-pound person sits 1.8 meters from the center
of the seesaw, how far should a 125-pound person sit from the center to balance the seesaw?
21. SWIMMING Logan and Brianna each bought a pool membership. Their average cost per day is inversely
proportional to the number of days that they go to the pool. Logan went to the pool 25 days for an
average cost per day of $5.60. Brianna went to the pool 35 days. What was her average cost per day?