algebra 5.1 identifying linear functions. learning targets language goal students will be able to...
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ALGEBRA 5.1
Identifying Linear Functions
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Learning Targets
Language Goal Students will be able to identify linear
functions and linear equations.Math Goal Students will be able to graph linear
functions that represent real-world situations and give their domain and range.
Essential Questions What is a real-world situation that represents
a linear function?
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Warm-up
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Vocabulary
Linear Function:
Linear Equation:
A function whose graph forms a straight line.
Any equation that can be written in standard form.
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Identifying Linear Functions
There are 3 ways to identify. By its Graph By using Ordered Pairs By its Equation
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Identifying by its Graph
Your first step is to identify if the graph is a function Remember a function is when one domain
value is paired with exactly one range value.
You can do the vertical line test!
If the graph is a function, tell whether it is linear. A linear graph means that it forms a
straight line.
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Identifying by its Graph
Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear?
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
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Example 1: Your Turn!
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
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Identifying by using Ordered Pairs It might help to write all ordered pairs into a
table. For example: {(2, 5), (4, 8), (6, 11)}
In a linear function, a constant change in x corresponds to a constant change in y.***Remember both x and y need to have a constant change in values. It does not have to be the same
constant!
X Y
2 5
4 8
6 11
+2+2
+3+3
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Identifying by using Ordered Pairs
X Y
-2 7
-1 4
0 1
1 -2
2 -5
Example Non Example
X Y
-2 6
-1 3
0 2
1 3
2 6
+1+1+1+1
- 3
- 3
- 3
- 3
+1+1+1+1
- 3
- 1
+1+3
Constant change in x and y
Linear Function
Constant change in x and but not y
Not a linear function
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Identifying by using Ordered Pairs Tell whether each set of ordered pairs
satisfies a linear function. Explain.A. {(2, 4). (5, 3), (8, 2), (11, 1)} B.{(-10, 10), (-5, 4), (0 2), (5, 0)}
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Example 2: Your Turn!
Tell whether each set of ordered pairs satisfies a linear function. Explain.
C. {(3, 5). (5, 4), (7, 3), (9, 2), (11, 1)} D.{(0, -3), (4, 0), (8, 3), (12, 6), (16, 9)}
E. {(-4, 13), (-2, 1), (0, -3), (2, 1), (4, 13)}
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Identifying by using the Equation If an equation can be written in standard
form, then it is a linear equation.
What is standard form?
Ax + By = C where A, B, and C are real numbers and A and B are not
both 0.
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Identifying by using the Equation Notice that when a linear equation is
written in standard form… x and y both have exponents of 1 x and y are not multiplied together x and y do not appear in denominators,
exponents or radical signs.
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Identifying by using the Equation
Linear Not Linear (Standard Form)
(can be written as
(can be written as
x and y are multiplied
x has an exponent other than 1
y is in a denominator
Standard Form: Ax + By = C
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Practice Re-Writing in Standard Form
1. 2.
3.
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Identifying by using an Equation Tell whether each function is linear.
1. 2. 3. y = 12
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Identifying by using an Equation Tell whether each function is linear. If yes
graph the function.
A. B. y = 12 C. D.
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Example 3: Your turn
Tell whether each function is linear. If yes graph the function.
A. B. C. D.
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Review
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Word Application
Sue rents a manicure station in a salon and pays the salon owner $5.50 for each manicure she gives. The amount she pays each day is given by f(x) = 5.50x, where x is the number of manicures. Graph the function and give its domain and range.
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Word Application
The relationship between human years and dog years is given by the function y = 7x, where x is the number of human years. Graph this function and give its domain and range.
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