Linear Equations Make-up

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

 $\left|x\ +\ 5\right|\ =\ 43$  

• Linear

• Nonlinear

Multiple Choice

 $\frac{x}{5}\ -^{ }65\ =y$  

• Linear

• Nonlinear

Multiple Choice

 $y=x^4$  

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Non-Linear

Multiple Choice

 $y\ =\ 6x\ +\ 5$  

• Linear

• Nonlinear

Multiple Choice

 $y=\frac{6}{x^2}\$  

• Linear

• Nonlinear

CROC in tables, graphs, and equations

​

CROC stands for...

• Constant

• Rate

• of

• Change

CROC in Tables

To find the CROC in a table, find the change in y divided by the change in x.

Multiple Choice

Find the rate of change in the table.

• 3

• -3

• 20

• Not a constant rate/Non-Linear

Multiple Choice

What is the constant rate of change?

• Not here.

• $80 per month.

• $82 per month.

• $41 per month.

Multiple Choice

What is the rate of change for this table?

• 1/9

• 9

• 8

• 1/8

Multiple Choice

Calculate the rate of change.

• 6

• 1/6

• -6

• -1/6

CROC in Graphs

To find the CROC in a graph, find the change in y divided by the change in x.

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Multiple Choice

Find the slope of the line.

• 1/4
• -1/4
• -4/1
• 4/1

Multiple Choice

Find the slope:

• 2
• -2
• 1/2
• -1/2

Multiple Choice

Find the slope of the graphed line.

•  $\frac{3}{7}$  

•  $-\frac{3}{7}$  

•  $\frac{7}{3}$  

•  $-\frac{7}{3}$  

Multiple Choice

What type of slope is shown by the stairs in the image?

• positive

• negative

• undefined

• zero

Multiple Choice

find the slope

• 3/2

• -3/2

• (-0,-3)

• none of the above

Multiple Choice

find the slope

• 3/2

• -3/2

• (-0,-3)

• none of the above

CROC in Equations

To find the CROC in a equation, find the coefficient next to x.

Multiple Choice

If the constant rate of change is 10, which of the following is the correct proportional equation?

• 10=kx

• 10=k

• y=10k

• y=10x

Multiple Choice

In the equation y = 14x, what is the constant rate of change?

• y

• x

• 14

Multiple Choice

In the equation y = 14x, what is the constant rate of change?

• y

• x

• 14

Slope Intercept with Real World Graphs

We are practicing on slope and slope-intercept

Real Life Linear Equations

• y - intercept (0,32)

• These means that the starting fee for renting the car is $32

Multiple Choice

What is the meaning of the y-intercept of this graph?

• when the gas take is empty

• starting amount of gas

• rate at which the gas take empties

• the starting mileage

The rate of change of this graph

Multiple Choice

Which slope-intercept equation matches the graph?

• $$y=\frac{3}{2}x+2$$

• $$y=\frac{2}{3}x-3$$

• $$y=\frac{2}{3}x+2$$

• $$y=\frac{3}{2}x-3$$

Rate of change (slope)

Multiple Choice

What is the situation of the linear graph?

• The beaker is being filled.

• The beaker is being emptied.

• The beaker is remaining the same amount

Multiple Select

Select ALL statements below that are TRUE.

• slope

  $$-\frac{1}{3}$$

• y-intercept (0,1)
  

• y-intercept (0,0)
  

• slope -3
  

Money Earned Selling Programs

• Ken got a job selling programs.

• He starting payment is $15

• y-intercept (0,15)

• He earns $0.50 per program sold

• slope (rate of change) $0.50 per program

Multiple Choice

Which slope intercept equation matches the graph?

• $$y=4x+4$$

• $$y=4x-1$$

• $$y=\frac{1}{4}x+4$$

• $$y=-4x+4$$

Donations

• Tanya has a donation plan of $4 to start and $2 per mile.

• Charlie has a donation plan of $10 to start and $0.50 per mile

Multiple Choice

Which equation represents this situation: Rocky's Canoe Rental charges a flat fee of $25 and $30 per hour?

• $$y=25x+30$$

• $$y=30x+25$$

• $$y=55x$$

• $$y=30x-25$$

Drew's Scuba Tank

Multiple Choice

What is the slope-intercept equation of the graph?

• $$y=-x-5$$

• $$y=5x$$

• $$y=x-5$$

• $$y=x+5$$

Multiple Choice

Which equation represents this situation:

Pappy's Pizza charges $8 for a plain cheese pizza and $1.50 per topping.

• $$y=1.50x+8$$

• $$y=8x+1.50x$$

• $$y=8x+1.5$$

• $$y=9.50x$$

What can you tell me about the graph?

• y-intercept?

• What does it mean?

• rate of change?

Multiple Choice

What is the starting temperature in the tank?

• 82 degrees

• 100 degrees

• 5 degrees

• 80 degrees

Multiple Choice

What is the meaning of the coordinate (4, 74)?

• At 74 hours, the temperature of the tank is 4 degrees.

• At 4 hours, the temperature of the tank is 74 degrees.

• After 4 hours the temperature of the take is 47 degrees.

Multiple Choice

The y-intercept, b (also called the vertical intercept), tells us where the line crosses the ___________.

• y-axis

• x-axis

• the second quadrant

• the fourth quadrant

Multiple Choice

If m > 0, the line_____________________ left to right.

• rises

• falls

• decreases

• curves

Multiple Choice

If m < 0, the line ______________________left to right. 3.

• rises

• falls

• increases

• curves

Multiple Choice

The larger the value of |m| is, the____________________ the graph.

• steeper

• more shallow

• flatter

Multiple Choice

The Slope, m, of a line y = mx + b gives the _______________ of y with respect to x.

• rate of change

• change

• y-intercept

• initial value

Multiple Choice

Find the initital value

• 20

• 0

• 17

• 1

Multiple Choice

Find the rate of change.

• -2 minutes per gallon
• -20 minutes per gallon
• -2 gallons per minute
• -20 gallons per minute

Multiple Choice

Which equation best represents the relationship between x and y in the table shown?

• y= 5x+5

• y=1/5x+5

• y=15x+5

• y=10x+5

Multiple Choice

Bob has $150 in his savings account and saves $40 per month.

• y=150 + 40

• y=40x + 150

• y=150x + 40