Study Guide and Intervention (continued) - MathnMind

12-1
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Inverse Variation
Use Inverse Variation If two points (x 1 , y 1 ) and (x 2 , y 2 ) are solutions of an inverse
variation, then x 1 y 1 k and x 2 y 2 k.
Product Rule or Inverse Variation the equation x 1 y 1 x 2 y 2
From the product rule, you can form the proportion .
Example
If y varies inversely as x and y 12 when x 4, find x when y 18.
Method 1 Use the product rule.
x1 y1 x2 y2 4 12 x2 18 x1 4, y1 12, y2 18
48
x2 Divide each side by 18.
18
8
3
x 2
Exercises
Product rule for inverse variation
Simplify.
8
Both methods show that x2 when y 18.
3
© Glencoe/McGraw-Hill 706 Glencoe Algebra 1
x1
x2
y2
y1
Method 2 Use a proportion.
x1 y2
x2 y1
4
x2
Proportion for inverse variation
x 1 4, y 1 12, y 2 18
48 18x 2
8
3
18
12
x 2
Cross multiply.
Simplify.
Write an inverse variation equation that relates x and y. Assume that y varies
inversely as x. Then solve.
1. If y 10 when x 5, 2. If y 8 when x 2,
find y when x 2. find y when x 4.
3. If y 70 when x 7, 4. If y 1.5 when x 0.5,
find y when x 5. find x when y 3.
5. If y 100 when x 120, 6. If y 16 when x 4,
find x when y 20. find x when y 32.
7. If y 7.5 when x 25, find y when x 5.
1
1
1
8. If y when x , find y when x . 2
8
2
3
5
1
9. If y when x , find y when x . 4
4
2
10. DRIVING The Gerardi family can travel to Oshkosh, Wisconsin, from Chicago, Illinois,
in 4 hours if they drive an average of 45 miles per hour. How long would it take them if
they increased their average speed to 50 miles per hour?
11. GEOMETRY For a rectangle with given area, the width of the rectangle varies inversely
as the length. If the width of the rectangle is 40 meters when the length is 5 meters, find
the width of the rectangle when the length is 20 meters.