Page 96 - Math Course 3 (Book 1)

Rate of Change and Direct Variation

Let’s Begin Your Turn!

Use Direct Variation to Solve Problems

BUSINESS
Use Direct Variation to Solve Problems The graph shows the number of frequent cus-
tomer points a book store customer receives for
Example each dollar spent in the store. Write an equation
that relates the spending s and the points p. Then
predict how many points a customer receives for a
LANDSCAPING purchase of $34.40.
As it is being dug, the depth of a wide hole for a Shipping($) Points
backyard pond is recorded on a table. Write an
equation that relates time and hole depth. 10.60 53

Time (min) Hole Depth (in.) 15.80 79

x y 22.20 111
10 8 28.60 143
20 15 A. p = 5s; 172
B. p = 5s; 220
30 24 C. s = 5p; 172
40 32 D. s = 5p; 220

Step 1
Find the value of k using the equation y = kx. Answer
Choose any point in the table. Then solve for k.

y = kx Direct variation

8 = k(10) Replace y with 8 and x with 10.
8
= k Divide each side by 10.
10
0.8 = k Simplify

Step 2 Use k to write an equation.
y = kx Direct variation

y = 0.8x Replace k with 0.8.

Answer y = 0.8x

Predict how long it will take to dig a depth of 36
inches.

y = 0.8x Write the direct variation equation.
36 = 0.8x Replace y with 36.
36
= x Divide each side by 0.8.
0.8
45 = x Simplify.

Answer 45 minutes

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