Linear Functions

Linear Functions

Introduction

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Definition of a Linear Function

• A linear function is any function that graphs to a straight line. 

• A function has either one or two variables with no exponents or powers

• If the function has more variables, the variables must be constants or known variables for the function to remain a linear function.

Identifying Linear Functions

• It must have either one or two real variables.

•  If another variable is present, it must be a known variable or constant. For example, the function C = 2 * pi * r is a linear function because only the C and r are real variables, with the pi being a constant.

• none of the variables can have an exponent or power to them.  All variables must be in the numerator.

•  function must graph to a straight line. Any kind of a curve disqualifies the function.

Multiple Choice

Is the equation y=x^2 linear? Why, or why not?

• No, because the x variable has an exponent.

• No, because the value of y has not been defined.

• Yes, because it's an equation with two variables.

• Yes, because the y variable has no exponent.

Multiple Choice

What is the minimum number of points needed to graph a linear function?

• Three points

• Two points

• One Points

• Zero points

Multiple Choice

For the linear function h=2t-1, what is h when t=4?

• -7

• 7

• 8

• 10

Multiple Choice

A linear function must graph to a _____ line.

• stepped

• curved

• straight

• parabolic

Multiple Choice

Is y=2x+D-10 linear if given that D=4?

• No

• Yes

• Sometimes

What is a Rate of Change?

Rate that describes how one quantity changes in relation to another quantity

If x is the independent variable and y is the dependent variable, then. rate of change=change in y change in x

What is a SLOPE?

slope of real-world situations is often referred to as rate of change.

Rate of change” means the same as “slope.”

 If you are asked to find the rate of change, use the slope formula or make a slope triangle

Types of Slopes of a Line

Positive Slope

A positive slope means the line is increasing when viewed from left to right.


As you can see, Mr. Piggy is having a hard time going up since it costs him an extra effort for an uphill climb.

Negative Slope

A negative slope means the line is decreasing when viewed from left to right.

Thanks to gravity, Mr. Piggy is definitely enjoying the slide because it takes him less effort to go down.

Zero Slope

A zero slope means the line is neither increasing nor decreasing when viewed from left to right, or vice versa. 

Simply put, the slope of a horizontal line is zero,

Undefined Slope

An undefined slope or infinite slope, means the line is neither moving to the left nor to the right such as the case of a vertical line. The slope of a vertical line is either + \,\infty+∞ or - \,\infty−∞.

Types of Slopes

Identify if the Slope is positive, Negative, Zero or Undefined

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Multiple Choice

What is the slope of this line?

• positive

• negative

• zero

• undefined

Multiple Choice

What is the slope of this line?

• positive

• negative

• zero

• undefined

Multiple Choice

What is the slope of this line?

• positive

• negative

• zero

• undefined

Multiple Choice

What is the slope of this line?

• positive

• negative

• zero

• undefined

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Multiple Choice

Calculate the rise and run to find the slope of this line.

• 
  

   $-\frac{5}{3}$  

•  $\frac{5}{3}$  

•  $\frac{3}{5}$  

•  $-\frac{3}{5}$  

Multiple Choice

Calculate the rise and run to find the slope of this line.

• 4

• 3

• 2

• 1

Multiple Choice

Calculate the rise and run to find the slope of this line.

• $\frac{1}{3}$

• $\frac{1}{4}$

• $-\frac{1}{4}$

• $-\frac{1}{3}$

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