Page 129 - Math Course 3 (Book 1)

Direct Variation Equation

Real World Example Your Turn!

TRAVEL
The Ramirez family is driving cross-country on Write and Solve a Direct Variation Equation
vacation. They drive 330 miles in 5.5 hours.
Suppose y varies directly as x, and y = 15 when
Write a direct variation equation to find the distance x = 5. Write a direct variation equation that relates
driven for any number of hours. x and y.

A. y = 3x
Word Distance equals rate times time. B. y = 15x
C. y = 5x
Variable Let r = rate. D. y = 45x

Equation 330 mi = r × 5.5h Answer

Solve for the rate. Suppose y varies directly as x, and y = 15 when
x = 5. Use the direct variation equation to find x
330 = r (5.5) Original equation when y = –45.

330 = r ( 5.5) Divide each side by 5.5. A. –3
5.5 5.5 B. 9
60 = r Simplify. C. –15
D. –5
Therefore, the direct variation
Answer
equation is d = 60t.
Answer
Graph the equation.

The graph of d = 60t passes through the origin with Real World Example
a slope of 60.
60 rise Dustin ran a 26-mile marathon in 3.25 hours. Write
m = a direct variation equation to find the distance run
1 run
for any number of hours.
Travel Time
Answer 500 A. d = h
d
Distance (miles) 400 C. d = 8
B. d = 8h
300
1
D. d = h
200
8
100
0 1 2 3 4 5 6 t Answer
Time (hours)
Estimate how many hours it would take to jog 16
Estimate how many hours it would take to drive 600 miles.
miles.

A. 1 hour
d = 60t Original equation 1
600 = 60t Replace d with 600. B. hour
2
600 = 60t Divide each side by 60. C. 16 hours
60
60
10 = t Simplify. D. 2 hours

At this rate, it will take 10 hours to Answer
Answer
drive 600 miles.
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