5-2 Slope and Direct
Variation
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Objectives
• Students will write and graph direct
variation equations.
• Students will solve problems involving
direct variation.
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Vocabulary
• direct variation – an equation of the form y =
kx, where k ≠0. We say that y varies directly
as x or y varies directly with x.
• In the equation y = kx, k is the constant of
variation.
• family of graphs – includes graphs and
equations of graphs that have at least one
characteristic in common.
• parent graph- the simplest form of the graph in
a family.
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Direct Variation Graphs
• If k >0, the slope is positive.
• If k<0, the slope is negative.
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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.
Slope formula
Simplify.
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Answer: The constant
of variation is 2.
The slope is 2.
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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.
Slope formula
Simplify.
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Answer: The constant
of variation is –4.
The slope is –4.
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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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Step 1
Write the slope as
a ratio.
Step 2
Graph (0, 0).
Step 3
From the point (0, 0), move down 3 units and
right 2 units. Draw a dot.
Step 4
Draw a line containing the points.
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Use the direct variation equation to find x when
Direct variation equation
Replace y with 15.
Divide each side by –3.
Simplify.
Answer: Therefore,
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when
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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
Equation
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330 mi
equals
rate
times
r
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time.
5.5h
10
Solve for the rate.
Original equation
Divide each side by 5.5.
Simplify.
Answer: Therefore, the direct variation equation is
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Graph the equation.
The graph of
slope of 60.
passes through the origin with a
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 distance
ran for any number of hours.
Answer:
b. Graph the
equation.
Answer:
c. Estimate how many hours it would take to jog 16 miles.
Answer: 2 hours
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