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Example 1 Slope and Constant of Variation
Example 2 Direct Variation with k > 0
Example 3 Direct Variation with k < 0
Example 4Write and Solve a Direct Variation Equation
Example 5 Direct Variation Equation
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Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is 2. The slope is 2.
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Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is –4. The slope is –4.
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Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
a. Answer: constant ofvariation: 4; slope: 4
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Answer: constant ofvariation: –3; slope: –3
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
b.
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Step 1 Write the slope as a ratio.
Step 2 Graph (0, 0).
Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot.
Step 4 Draw a line containing the points.
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Answer:
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Step 1 Write the slope as a ratio.
Step 2 Graph (0, 0).
Step 3 From the point (0, 0), move down 3 units andright 2 units. Draw a dot.
Step 4 Draw a line containing the points.
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Answer:
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Suppose y varies directly as x, and when
Write a direct variation equation that relates x and y.
Find the value of k.
Direct variation formula
Replace y with 9 and x with –3.
Divide each side by –3.
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Simplify.
Answer: Therefore,
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Use the direct variation equation to find x when
Direct variation equation
Answer: Therefore, when
Replace y with 15.
Divide each side by –3.
Simplify.
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Suppose y varies directly as x, and when
a. Write a direct variation equation that relates x and y.
b. Use the direct variation equation to find x when
Answer: –15
Answer:
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Travel The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours.
Write a direct variation equation to find the distance driven for any number of hours.
Words The distance traveled is 330 miles, and the time is 5.5 hours.
Variables
Distance equals rate times time.
Equation 330 mi r 5.5h
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Solve for the rate.
Answer: Therefore, the direct variation equation is
Original equation
Divide each side by 5.5.
Simplify.
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Graph the equation.
The graph of passes through the origin with a slope of 60.
Answer:
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Estimate how many hours it would take to drive 600 miles.
Original equation
Replace d with 600.
Divide each side by 60.
Simplify.
Answer: At this rate, it will take 10 hours to drive 600 miles.
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Dustin ran a 26-mile marathon in 3.25 hours.
a. Write a direct variation equation to find the distanceran for any number of hours.
b. Graph the equation.
Answer:
Answer:
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c. Estimate how many hours it would take to jog 16 miles.
Answer: 2 hours