Linear Equations and Functions

Linear and Non-Linear Functions

​

Linear Functions...

are straight lines on a graph

Linear Functions...

have a constant rate of change

Linear Functions...

are represented by equations that have:

* no exponents

* no absolute value signs

* fractions with variables only in the numerator

Non-Linear Functions...

have curves or

two or more different slopes

Non-Linear Functions...

do not have a constant rate of change

Nonlinear Functions...

are represented by equations that have:

* exponents

* absolute value signs

* fractions with variables in the denominator

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

Does the first table represent a linear or nonlinearn function?

• linear

• nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

$$\frac{x}{5}\ -65\ =y$$

Linear or Nonlinear? 

• Linear

• Nonlinear

Multiple Choice

$$y=x^4$$  

Linear or Nonlinear? 

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

$$y\ =\ 6x\ +\ 5$$  

Linear or Nonlinear? 

• Linear

• Nonlinear

Multiple Choice

$$y=\frac{6}{x^2}\$$  

Linear or Nonlinear? 

• Linear

• Nonlinear

Slope

Topics in this quizizz:

- Identifying slope (direction)

- Finding slope of a line (steepness)

- Slope from a Table

- Slope from an Equation

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Multiple Choice

What type of slope?

• positive

• negative

• zero

• undefined

Multiple Choice

What type of slope?

• negative
• steep
• undefined
• zero slope

Multiple Choice

What type of slope?

• zero slope
• undefined
• negative
• positive

Multiple Choice

What type of slope?

• undefined
• positive slope
• negative slope
• zero slope

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $\frac{2}{3}$

• $\frac{3}{2}$

• 3

• $\frac{1}{3}$

Multiple Choice

Find the slope of the line below using rise/run.

•  $\frac{1}{2}$  

•  $\frac{2}{1}$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• 3

•  $\frac{1}{3}$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

•  $\frac{5}{3}$  
  

•  $\frac{3}{5}$  
  

• 5

•  $\frac{5}{4}$  
  

Multiple Choice

Find the slope of the line below using rise/run.

•  $\frac{1}{2}$  
  

•  $\frac{4}{2}$  
  

• 2

• 3

•  $\frac{2}{3}$  

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $\frac{2}{5}$

• $\frac{5}{2}$

• $2\ \frac{1}{2}$

• 2

Multiple Choice

Find the slope. Simplify, if you can.

•  $\frac{1}{2}$  
  

•  $\frac{4}{8}$  

• 4

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• 3

•   $\frac{1}{3}$  

•  $-\frac{1}{3}$  

• -3

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

Identify the slope in the equation:

 $y=8x$  

• 8

• 1/8

• -8

• 0

Multiple Choice

Identify the slope in the equation:

 $y=\frac{5}{6}x$  

•  $\frac{5}{6}$  

•  $\frac{6}{5}$  
  

• 5

• 6

Slope-intercept form: y=mx+b

y=mx+b

Slope-intercept form is a format we use to write the equation of a line.

each letter represents something different

m = slope

b= y-intercept

y= all the y-coordinate values on the line

x= all the x-coordinate values

Multiple Choice

What does "b" represent in y=mx+b?

• slope

• y-intercept

• all the y-coordinate values on the line

• all the x-coordinate values on the line

Multiple Choice

What does "m" represent in y=mx+b?

• slope

• y-intercept

• all the y-coordinate values on the line

• all the x-coordinate values on the line

Multiple Choice

What does "m" represent in y=mx+b?

• slope

• y-intercept

• all the y-coordinate values on the line

• all the x-coordinate values on the line

Identifying m & b in equations (y=mx+b)

• y= 4x - 3 ..... m= 4 , b= -3

• y = -3x + 7 ..... m= -3 , b= 7

• y = x - 8 ..... m= 1 , b= -8

• y = -x ..... m= -1 , b= 0

• y = 5x + 10 ..... m= 5 , b= 10

Multiple Choice

y = -7x +9

Identify the slope

• m= 9

• m=-7

• m= 7x

• m= -7x

Multiple Choice

y = -7x +9

Identify the y-intercept

• b= 9

• b=-7

• b= 7x

• b= -7x

Multiple Choice

y = -x -10

Identify the m & b

• m= -x , b= -10

• m= -x , b= 10

• m= -1 , b= -10

• m= -1 , b= 10

Multiple Choice

Which equation is slope intercept form?

• y = mx + b

• $$\frac{y_2-y_1}{x_2-x_1}$$  

• ax + by = c

• $$A\ =\ \pi r^2$$  

Multiple Choice

Which equation is in slope intercept form?

• y - 3 = x + 3

• y = 3x - 1

• y = 3x -6 y

• $$y\ =\ \frac{4}{x}$$  

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6
• y=3x-6
• y=3x+6
• y=6x+3

U4L4 X and Y Intercepts

What is an intercept?

• x-intercepts are where the line crosses the x-axis

• y-intercepts are where the line crosses the y-axis

Multiple Choice

Is the point (3, 0) an x-intercept, a y-intercept, both, or neither?

• x-intercept

• y-intercept

• both

• neither

Multiple Choice

Is the point (0, -5) an x-intercept, a y-intercept, both or neither?

• x-intercept

• y-intercept

• both

• neither

Multiple Choice

Is the point (5, 5) an x-intercept, a y-intercept, both or neither?

• x-intercept

• y-intercept

• both

• neither

Multiple Choice

What is the point (0, 0)?

• x-intercept

• y-intercept

• both

• neither

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Interpret the x-intercept

• (12, 0)

  After 12 haircuts, Adrienne will make a profit of $0

• (0, –200)

  Before any haircuts are given, Adrienne's starting profit is –$200

Multiple Choice

Interpret the y-intercept

• (12, 0)

  After 12 haircuts, Adrienne will make a profit of $0 (breakeven)

• (0, –200)

  Before any haircuts are given, Adrienne's starting profit is –$200

Open Ended

Why might Adrienne be starting with a -$200 profit?

Multiple Choice

Interpret the x-intercept

• (8, 0)

  After 8 weeks, there is $0 in the account (they're broke)

• (0, 350)

  Jazz started with $350 in the account

Multiple Choice

Interpret the y-intercept

• (8, 0)

  After 8 weeks, there is $0 in the account

• (0, 350)

  Jazz started with $350 in the account