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How can you determine whether a function is linear or nonlinear?

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Presentation on theme: "How can you determine whether a function is linear or nonlinear?"— Presentation transcript:

1 How can you determine whether a function is linear or nonlinear?
3.2 Linear Functions How can you determine whether a function is linear or nonlinear? Students will be able to determine whether functions are linear functions by using graphs, tables and equations.

2 Students will be able to determine whether functions are linear functions by using graphs, tables and equations. A linear equation in two variables, x and y, is an equation that can be written in the form 𝑦=𝑚𝑥+𝑏, where m and b are constants (just numbers). Likewise, a linear function is a function whose graph is a non-vertical line. A linear function has a constant rate of change and can be represented by a linear equation in two variables. A nonlinear function does not have a constant rate of change and its graph is not a line.

3 Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the graph represent a linear or nonlinear function? Explain. The function is nonlinear. Because the graph is not a line. The function is linear. Because the graph is a line.

4 Does the table represent a linear or nonlinear function? Explain.
Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the table represent a linear or nonlinear function? Explain. A linear function has a constant rate of change +3 +3 +3 As x increases by 3, y decreases by 6. The rate of change is constant for both x and y. The function is linear. x 3 6 9 12 y 36 30 24 18 -6 -6 -6

5 Does the table represent a linear or nonlinear function? Explain.
Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the table represent a linear or nonlinear function? Explain. A linear function has a constant rate of change +2 +2 +2 As x increases by 2, y increases by different amounts. The rate of change is not constant for both x and y. The function is nonlinear. x 1 3 5 7 y 2 9 20 35 +7 +11 +15

6 You try!! Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the graph represent a linear or nonlinear function? Explain. The function is linear. Because the graph is a line. The function is nonlinear. Because the graph is not a line.

7 Does the table represent a linear or nonlinear function? Explain.
You try!! Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the table represent a linear or nonlinear function? Explain. A linear function has a constant rate of change +1 +1 +1 As x increases by 1, y increases by 2. The rate of change is constant for both x and y. The function is linear. x 1 2 3 y 5 7 9 +2 +2 +2

8 Does the table represent a linear or nonlinear function? Explain.
You try!! Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the table represent a linear or nonlinear function? Explain. A linear function has a constant rate of change +1 +1 +1 As x increases by 1, y decreases by different amounts. The rate of change is not constant for both x and y. The function is nonlinear. X 1 2 3 4 y 16 8 -8 -4 -2

9 Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Which of the following equations represent linear functions? Explain. A linear function can be written in the form 𝑦=𝑚𝑥+𝑏, where m and b are constants (just numbers). 𝑦=3.8, 𝑦= 𝑥 , 𝑦= 3 𝑥 , 𝑦= 2 𝑥 , 𝑦=6(𝑥−1), and 𝑥 2 −𝑦=0 You cannot rewrite the equations 𝑦= 𝑥 , 𝑦= 3 𝑥 , 𝑦= 2 𝑥 , and 𝑥 2 −𝑦=0 in the form 𝑦=𝑚𝑥+𝑏. So these equations cannot represent linear functions. You can rewrite the equation 𝑦=3.8 as 𝑦=0𝑥+3.8 You can rewrite the equation 𝑦=6(𝑥−1) as 𝑦=6𝑥−6 So these equations represent linear functions.

10 You try!! Students will be able to determine whether functions are linear functions by using graphs, tables and equations. Does the equation represent a linear or nonlinear function? Explain. A linear function can be written in the form 𝑦=𝑚𝑥+𝑏. 𝑦=𝑥+9 𝑦= 3𝑥 5 𝑦=5− 𝑥 2 You can rewrite the equation as 𝑦=1𝑥+9 Equation represents a linear function. You can rewrite the equation as 𝑦= 3 5 𝑥+0 Equation represents a linear function. You cannot rewrite the equation as 𝑦=𝑚𝑥+𝑏 Equation is a nonlinear function.

11 So let’s review! What have we covered so far? Students will be able to determine whether functions are linear functions by using graphs, tables and equations. In a graph it looks like a …… Line In a table we look for what? A constant rate of change in both x and y values. In equations we need to be able to do what? Write the equation in the form of 𝑦=𝑚𝑥+𝑏


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