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Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions
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Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Jan 13, 2016

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Page 1: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Identify linear functions and linear equations.

Graph linear functions that represent real-world situations.

Clear Targets

Linear Functions

Page 2: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

linear functionlinear equation

Vocabulary

Page 3: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight line. A function with a graph that forms a straight line is called a linear function.

Page 4: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

Each domain value is paired with exactly one range value. The graph forms a line.

linear function

Page 5: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

Each domain value is paired with exactly one range value. The graph is not a line.

not a linear function

Page 6: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

The only domain value, –2, is paired with many different range values.

not a function

Page 7: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

Each domain value is paired with exactly one range value. The graph forms a line.

linear function

Page 8: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

Each domain value is paired with exactly one range value. The graph forms a line.

linear function

Page 9: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Does the graph represent a function? A linear function?

Each domain value is not paired with exactly one range value.

not a function

Page 10: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

You can sometimes identify a linear function by looking at a table or a list of ordered pairs. In a linear function, a constant change in y corresponds to a constant change in x.

Page 11: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

In this table, a constant change of –3 in y corresponds to constant change of +1 in x . These points satisfy a linear function.

The points from this table lie on a line.

Page 12: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

In this table, there is not a constant change in the y, as the x increases by one. These points do not satisfy a linear function.

The points from this table do not lie on a line.

Page 13: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

+4+4+4+4

+3+3+3+3

x y

0 4 81216

–3 0 3 6 9

Tell whether the set of ordered pairs satisfies a linear function. Explain.

{(0, –3), (4, 0), (8, 3), (12, 6), (16, 9)}

Write the ordered pairs in a table.

Look for a pattern.

A constant change of +3 in y corresponds to a constant change of +4 in x.

These points satisfy a linear function.

Page 14: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

+2+2+2+2

–12–4+4+12

x y

–4 –2 024

131

–3 113

{(–4, 13), (–2, 1), (0, –3), (2, 1), (4, 13)}

Write the ordered pairs in a table.

Look for a pattern.

There are different changes in y as x increases by a constant 2.

These points do not satisfy a linear function.

Tell whether the set of ordered pairs satisfies a linear function. Explain.

Page 15: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Tell whether the set of ordered pairs {(3, 5), (5, 4), (7, 3), (9, 2), (11, 1)} satisfies a linear function. Explain.

+2+2+2+2

–1–1–1–1

x y

3 5 7 911

5 4 3 2 1

Write the ordered pairs in a table.

Look for a pattern.

A constant change of -1 in y

corresponds to a constant change of +2 in x.

These points satisfy a linear function.

Page 16: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

f(x) = 7xx

1

2

3

f(1) = 7(1) = 7

f(2) = 7(2) = 14

f(3) = 7(3) = 21

Graph the ordered pairs.

(3,21)

(2,14)

(1,7)

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.

Page 17: Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Exit Slip: Does this data represent a linear function? State the function.

Closure

Linear FunctionsMin

Ft

1 7

2 9

3 11