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Algebra 5.55.5 Direct Variation
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Learning Targets
Language Goal Students will be able to verbally
express direct variation.Math Goal Students will be able to identify, write,
and graph direct variation.Essential Questions Why is direct variation a special type of
linear relationship?
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Warm-up
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Homework Check
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Homework Check
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Vocabulary
Direct Variation
Constant of Variation
A linear relationship that can be written in the form y = kx.
A nonzero constant (k) in a direct variation.
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Example 1: Identifying Direct Variation from Equations
Tell whether each equation represents a direct variation. (y = kx)
If so identify the constant of variation. (k)
You may have to solve for y first!A. y = 4x B. -3x + 5y = 0 C. 2x + y = 10
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Example 1: Identifying Direct Variation from Equations
Tell whether each equation represents a direct variation. (y = kx)
If so identify the constant of variation. (k)
You may have to solve for y first!D. 3y = 4x + 1 E. 3x = -4y F. y + 3x = 0
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Example 2: Identifying Direct Variations from Ordered Pairs
Tell whether each relationship is a direct variation. Explain.
Two methods to solve.
Method 1: Write an equation Method 2: Find for each ordered pair
x 1 3 5
y 6 18 30
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Why ?!
The direct variation equation is y = kx. Solve the equation for the constant k.
divide both sides by x.
**Therefore, by solving each ordered pair for k you can see if the constants are the same making it a direct variation.
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Example 2: Identifying Direct Variations from Ordered Pairs
Tell whether each relationship is a direct variation. Explain.
Method 1: Write an equation Method 2: Find for each ordered pair
x 2 4 8
y -2 0 4
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Example 2: Identifying Direct Variations from Ordered Pairs
Tell whether each relationship is a direct variation. Explain.
Method 1: Write an equation Method 2: Find for each ordered pair
x -3 1 3
y 0 3 6
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Example 2: Identifying Direct Variations from Ordered Pairs
Tell whether each relationship is a direct variation. Explain.
Method 1: Write an equation Method 2: Find for each ordered pair
x 2.5 5 7.5
y -10 -20 -30
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Example 3: Writing and Solving Direct Variation Equations
Again two methods.
Method 1: Find the value of k and then write the equation.
Method 2: Use a proportion.
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Example 3: Writing and Solving Direct Variation Equations
The value of y varies directly with x, and y = 6 when x = 12. Find y when x = 27.
Method 1: Method 2:
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Example 3: Writing and Solving Direct Variation Equations
The value of y varies directly with x, and y = 4.5 when x = 0.5. Find y when x = 10.
Method 1: Method 2:
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Example 3: Writing and Solving Direct Variation Equations
The value of y varies directly with x, and y = 3 when x = 9. Find y when x = 21.
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Example 4: Skipping
Not doing example 4.
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5.1 – 5.5 Quiz Tomorrow
Lets Review!
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5.1 – 5.5 Quiz Review
Identify whether the graph is a function.
If yes, is it linear?
Function?Linear?
Function?Linear?
Function?Linear?
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5.1 – 5.5 Quiz Review
Does the set of ordered pairs satisfy a linear function? Explain.
{(1, .5), (4, 1), (7, 1.5), (10, 2)}
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5.1 – 5.5 Quiz Review
Use intercepts to graph a line of the equation -6x – 3y = 24
Describe the correlation.
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5.1 – 5.5 Quiz Review
Find the x and y intercept from the graph below.
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5.1 – 5.5 Quiz Review
Find the slope of the following graph.
Rise: _______ Run:_______
Slope: ________
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5.1 – 5.5 Quiz Review
Draw a graph that has a positivie, negative, zero, or no correlation.
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5.1 – 5.5 Quiz Review
Find the slope between points (-4, 9) and (6, -5)
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5.1 – 5.5 Quiz Review
Find the slope of the linear function.
x y
-2 -4
0 -3
2 -2
4 -1
6 0
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5.1 – 5.5 Quiz Review
Find the slope of the line 6x + 8y =48
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5.1 – 5.5 Quiz Review
Tell whether the function is a direct variation or not. Explain.
A. y = 8x B. y = 2x + 1
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5.1 – 5.5 Quiz Review
The value of y varies directly with x. And y = 21 and x = 7. Find y when x = 4.
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5.1 – 5.5 Quiz Review
Come see me before school if you have any questions when studying.
Quiz is tomorrow!
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Lesson Quiz