1. Inverse Variation:2-2

2. Inverse Variation
“y varies inversely as x” means that as y increases x decreases and vice-versa.
Inverse variation equations are written as:
For example, the table shows
that the time needed to drive 600 miles decreases as speed increases.

3. Example 1: Writing Inverse Variation
Given: y varies inversely as x, and y = 4 when x = 5. Write the inverse variation function. k x
y =
y varies inversely as x. k 5
Substitute 4 for y and 5 for x.
4 =
k = 20
Solve for k. 20 x
Write the variation formula.
y =

4. To Solve an Inverse Variation
Write an inverse variation equation:
Substitute given values for y & x:
Solve for k:
Rewrite variation equation substituting only for k:
Substitute for given variable:
Solve for missing variable:

5. Example 2: Sports Application
The time t needed to complete a certain race varies inversely as the runner’s average speed s. If a runner with an average speed of 8.82 mi/h completes the race in 2.97 h, what is the average speed of a runner who completes the race in 3.5 h? k s
t =
Find k. k
8.82
2.97 =
Substitute.
k =
Solve for k. s
t =
Use for k. s
Substitute 3.5 for t.
3.5 =
Solve for s.
s ≈ 7.48

6. Example 3: k w d = Find k. k 55 2 = Substitute. k = 110 Solve for k.
The distance that the person on seesaw sits away from the fulcrum is inversely proportional to his weight. Nancy and Sam are trying to balance the seesaw. Sam, who weighs 55kg, is sitting 2m away from the fulcrum. How far away should Nancy, who weighs 50kg, be sitting to balance Sam? k w
d =
Find k. k 55
2 =
Substitute.
k = 110
Solve for k.
110 w
d =
Use 110 for k.
Substitute 50 for w.
110 50
d =
Solve for d.
d ≈ 2.2

7. Lesson Quiz
1. The weight w of a body above the Earth varies inversely as the square of the distance d from the center of the Earth. Write an inverse variation equation describing this situation.
2. The cost per person c of chartering a tour bus varies inversely as the number of passengers n. If it costs $22.50 per person to charter a bus for 20 passengers, how much will it cost per person to charter a bus for 36 passengers?
$12.50