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Algebra 5.55.5 Direct Variation
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?
Warm-up
Homework Check
Homework Check
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.
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
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
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
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.
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
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
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
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.
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:
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:
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.
Example 4: Skipping
Not doing example 4.
5.1 – 5.5 Quiz Tomorrow
Lets Review!
5.1 – 5.5 Quiz Review
Identify whether the graph is a function.
If yes, is it linear?
Function?Linear?
Function?Linear?
Function?Linear?
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)}
5.1 – 5.5 Quiz Review
Use intercepts to graph a line of the equation -6x – 3y = 24
Describe the correlation.
5.1 – 5.5 Quiz Review
Find the x and y intercept from the graph below.
5.1 – 5.5 Quiz Review
Find the slope of the following graph.
Rise: _______ Run:_______
Slope: ________
5.1 – 5.5 Quiz Review
Draw a graph that has a positivie, negative, zero, or no correlation.
5.1 – 5.5 Quiz Review
Find the slope between points (-4, 9) and (6, -5)
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
5.1 – 5.5 Quiz Review
Find the slope of the line 6x + 8y =48
5.1 – 5.5 Quiz Review
Tell whether the function is a direct variation or not. Explain.
A. y = 8x B. y = 2x + 1
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.
5.1 – 5.5 Quiz Review
Come see me before school if you have any questions when studying.
Quiz is tomorrow!
Lesson Quiz
