lesson 5-2 slope and direct variation. transparency 2 click the mouse button or press the space bar...
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Lesson 5-2
Slope and Direct Variation
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Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
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Objectives
• Write and graph direct variation equations
• Solve problems involving direct variation
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Vocabulary
• Constant of variation – the number k in equations the form y = kx
• Graph – is a plot of an ordered pair (x,y) on the coordinate plane
• Family of graphs – graphs and equations of graphs that have at least one characteristic in common
• Parent graph – the simplest of the graphs in a family of graphs
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y
x
y
x
x-y Coordinate Plane
Slope, m (∆y / ∆x)Point Plotting
(x, y) (-4, 7) (5, -8)
x – left or righty – up or down
right 5
down 8
left 4
up 7
(x, y) (-4, 7) (5, -8)
rise: ∆y – change in y (7 - -8 = 15)run: ∆x – change in x (-4 – 5 = -9)
∆y = 15
∆x = -9
5m = ------ -3
rise
run
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Example 1a
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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Example 1b
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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Example 2
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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Example 3
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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Example 4
Suppose y varies directly as x, and y = 9 when x = -3
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.
Simplify.
Answer: Therefore,
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Example 5
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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Example 5 cont
Solve for the rate.
Answer: Therefore, the direct variation equation is
Original equation
Divide each side by 5.5.
Simplify.
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Summary & Homework
• Summary:– A direct variation is described by an equation of
the form y = kx, where k ≠ 0– In y = kx, k is the constant of variation. It is also
the slope of the related graph
• Homework: – Pg 268 16-46 even