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
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?
Warm-up
Vocabulary
Linear Function:
Linear Equation:
A function whose graph forms a straight line.
Any equation that can be written in standard form.
Identifying Linear Functions
There are 3 ways to identify. By its Graph By using Ordered Pairs By its Equation
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.
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? _______
Example 1: Your Turn!
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
Function? __________
If yes, Linear? _______
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
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
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)}
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)}
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.
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.
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
Practice Re-Writing in Standard Form
1. 2.
3.
Identifying by using an Equation Tell whether each function is linear.
1. 2. 3. y = 12
Identifying by using an Equation Tell whether each function is linear. If yes
graph the function.
A. B. y = 12 C. D.
Example 3: Your turn
Tell whether each function is linear. If yes graph the function.
A. B. C. D.
Review
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.
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.
