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Linear vs. Non-linear

Math 8

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Vocabulary

Linear

- an equation that forms a single straight line when graphed

- must have a constant rate of change or slope between points

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Show whether each set of tables represents a linear relationship by finding several slopes. For each linear relationship write an equation in slope-intercept form.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Linear

Non-Linear

No Constant Rate of Change

 

None of these

are equal

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Determine whether the following graphs and equations are linear, or not linear. Tell the slope of any linear graph

Linear

a single straight line

 

Non-Linear

line is bent

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Make a table of values for the following equations and make a graph.

Determine whether the equation represents a linear relationship.

 

 

 

 

 

 

 

Non-Linear

this makes a curve

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Make a table of values for the following equations and make a graph.

Determine whether the equation represents a linear relationship.

 

 

 

 

 

 

Non-Linear

line is bent

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Make a table of values for the following equations and make a graph.

Determine whether the equation represents a linear relationship.

 

 

 

 

 

 

Non-Linear

this makes two curves

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Determine whether each equation is linear or non-linear. Explain

Non-Linear

Linear

equation is in

slope-intercept form

Linear

equation is in

slope-intercept form

Non-Linear

Non-Linear

x is under a radical symbol

creates a curve

x is attached to exponent

curve will form

Linear

equation is in

slope-intercept form

x is inside absolute value symbols

lines will bend

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- x or y is attached to exponent, absolute value symbols, radicals/roots, trigonometry functions, or if x is in the denominator of a fraction

What are the characteristics of Linear equations?

 

 

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What are the characteristics of Non-Linear equations?

 - can be written in Slope-Intercept Form

- can not be written in Slope-Intercept Form

- when graphed they make a straight line

- line will either bend or curve when graphed

- neither x or y is attached to symbols other than parentheses

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A square has a side length of s inches. The area of the square is a function of the side length. Graph the points you chose. Does this situation represent a linear or nonlinear function? Explain.

Non-Linear

line is forming a curve

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3

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5

6

10

 

Side Length

 

 

 

 

Area

 

has exponent

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