Functions

Functions

&

Linear Equations

​ MGSE8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Multiple Choice

A(n) __________ is an equation that forms a line when graphed.

• equation

• function

• relation

• linear equation

Multiple Choice

What is the Standard Form of a linear equation

• Ax+By=C

• y=mx+b

• y-y1 = m(x-x1)

• m = (y2-y1)/(x2-x1)

Standard Form : Ax + By = C

• Form is useful to convert to a different form.

• A, B, and C are all whole numbers.

Multiple Choice

What is Slope-Intercept Form of linear equations?

• Ax+By=C

• y=mx+b

• y-y1=m(x-x1)

• m = (y2-y1)/(x2-x1)

Multiple Choice

The ___________ is the point where a line crosses the x-axis.

• y-intercept

• x-intercept

• domain

• range

Multiple Choice

The y-intercept is the point where a line crosses the ___________.

• x-axis

• origin

• y-axis

• x-intercept

Multiple Choice

What is the slope in y=mx+b

• y

• m

• x

• b

Multiple Choice

What is the y-intercept in y=mx+b

• y

• m

• x

• b

Multiple Choice

Convert the following standard form equation to slope-intercept (y=mx+b).

• 2y = -6x + 24

• y = -3x + 12

Multiple Choice

Write the slope intercept form of the equation 3x - 2y = -16

• y = -3x - 8

• y = -3x + 8

• y = -3/2x - 8

• y = 3/2 x + 8

Multiple Choice

Write the slope intercept form of the equation 13x - 11y = -12

• y = 13/11x + 12/11

• y = 13x - 11

• y = -13/11x -12/11

• y = x + 1

Multiple Choice

Write the slope intercept form of the equation 9x - 7y = -7

• y = -9/7x + 1

• y = 9/7x + 1

• y = -9/7x - 7/9

• y = 9/7x + 7/9

Multiple Choice

What is the slope and y-intercept of the linear function given by the equation 7x + 2y = -28

• m = 7, b = 14

• m = -7/2, b = -14

• m = 7/2, b = 14

• m = 7, b = -14

Multiple Choice

What is the slope and y-intercept of the linear function given by the equation 2x + 3y = -6

• m = -2/3, b = -2

• m = 2, b = 2

• m = 2, b = -2

• m = 2/3, b = 2

Vertical and Horizontal Lines

Multiple Choice

What is the equation of a line with a zero slope that goes through the point
(6, 7) ?

• x = 6

• x = 7

• y = 6

• y = 7

HORIZONTAL LINE

EVERY point on a horizontal line has the same y-coordinate.

The line graphed is y = -4.

EVERY point on that line is (#,-4)

You can see some examples labeled on the graph.

Multiple Choice

If a line goes through the points (4, 5) and (4, 7), what type of line is it?

• Horizontal line

• Vertical line

• Slanted line

• No way to tell

VERTICAL LINE

EVERY point on a vertical line has the same x-coordinate.

The line graphed is x = 3.

EVERY point on that line is (3,#)

You can see some examples labeled on the graph.

Multiple Choice

What is the equation of a line with an undefined slope that goes through point
(-3,5)?

• x = -3
• x = 5
• y = -3
• y = 5

Multiple Choice

What is the equation of the line?

• y = 0
• y = 1
• y = 2
• x = 1

Multiple Choice

What is the equation of this line?

• x=5
• y=5
• y=5x
• x=-5

Multiple Choice

Vertical or horizontal?
Undefined slope

• vertical
• horizontal
• neither

Multiple Choice

Vertical or horizontal?
Slope of 0

• vertical
• horizontal
• neither

Multiple Select

Which points lie on the line y = -8?

• (0,-8)

• (116,-8)

• (-8.8)

• (-8,0)

• (-8,88)

Multiple Select

Choose ALL the correct statements that describe the line y = -5.

• The line passes through (0,-5).

• The line passes through (-5,0).

• The line is parallel to the x-axis.

• The line is parallel to the y-axis.

Multiple Select

Which points lie on the line y = -31?

• (100,-31)

• (16,-31)

• (-31,-31)

• (-31,0)

• (-31,8)

Multiple Select

Which points lie on the line x = 9?

• (9,0)

• (9,5)

• (9,-3)

• (0,9)

• (-9,9)

Point Slope Form

Multiple Choice

Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)

• Ax + By = C

• y = mx + b

• y=kx

y-y₁= m(x - x₁)

m= 2

(1, 6)

m is your slope

1 is your x value

6 is your y value

Plug in your values

y- 6= 2(x - 1)

Multiple Choice

What should be done to the put the equation y-2 = -4x + 16

into slope-intercept form (y=mx+b)?

• Subtract 16 from both sides

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by -2

Multiple Select

Select all of the following equations in point-slope form.

• y - 2 = 5(x - 2)

• 3x + 2y = 12

• y + 2 = 1/4(x + 4)

• y = 4x + 6

• 2y = 5x - 7

Multiple Choice

m= 5

(2, 4)

• y - 2= 5(x - 4)

• y - 4= 5(x - 2)

• y- 5 = 4(x - 2)

• y - 2 = 4(x - 5)

y - y₁= m(x - x₁)

When your COORDINATE has a negative value, you must change it to positive.

m=5

(-1, 2)

y - 2 = 5(x + 1)

Notice how at the end it was +1 because it was -1 as the x value.

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope:

(-2, -1); m= -3

• y + 1 = -3(x - 2)

• y + 1 = -3(x + 2)

• y - 1 = 3(x - 1)

• y + 2 = -3(x + 1)

Multiple Choice

The line with the equation

$$y+1=-3(x-5)$$ ,

contains the point ​ ​

• $$\left(5,-1\right)$$  

• $$\left(-5,1\right)$$  

• $$\left(5,1\right)$$  

• $$\left(1,5\right)$$  

Dropdown

The line with the equation

$$y+1=-3(x-5)$$ ,

and has a slope of ​

Select answer

Multiple Choice

The graph of linear function f passes through the point (1, -9) and has a slope of -3. What is the zero of f?

• 2

• 4

• -6

• -2

Multiple Choice

Explain how to graph the following equation...

y - 2 = 1/3(x - 3)

• Plot the point (−3,−2), move up 1 and right 3 units from there.

• Plot the point (3,2), move up 1 and left 3 units from there.

• Plot the point (3,2), move up 1 and right 3 units from there.

• Plot the point (2,3), move up 1 and right 3 units from there.

Writing Linear Equations from Two Points

Multiple Choice

What is the formula for finding slope?

• $$y=mx+b$$

• $$Ax+By=C$$

• $$\frac{y_2-y_1}{x_2-x_1}$$

Multiple Choice

Write the equation in slope intercept form of a line that passes through the given pair of points: (0,-1) and (2,1)

• y =x + 1

• y = x - 1

• y = -x + 1

• y = -x - 1

Multiple Choice

Find the slope in simplest form

• I have no clue how to do this

• 1/3

• 3

Multiple Choice

Find the equation of the line that passes through the points:
(0, -2) and (-5, 3)

• y = -x - 2

• y = x - 2

• y = x + 3

• y = -x - 3

Multiple Choice

Write the equation of the line that passes through the points
(3, 3) and (4, -1).

• y = -4x - 15

• y = 1/4x + 15

• y = -4x + 15

• y = -1/4x - 15

Multiple Choice

Which equation has a line that would pass through both (8, 5) and (9, −1) ?

• y = 6x + 53

• y = −6x - 53

• y = (−4/5)x + 53

• y = −6x + 53

Multiple Choice

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

• y= 8x - 5

• y= -8x + 25

• y= (1/8)x - 2

• y= (-1/8)x + 1

MGSE8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Multiple Select

Constant rate of change is the same thing as...

• slope

• y-intercept

Multiple Select

Which of the key words mean initial value? Select all that apply.

• begin

• per

• each

• start

Multiple Choice

A tub has 40 gallons of water in it and starts draining at a rate of 6 gallons per minute. Write a formula for the amount of water left in the tub.

• y = 6x + 40

• y = -6x + 40

• y = 6x - 40

• y = 40x - 6

Multiple Choice

A mechanic charges a flat fee of $15 and then charges $65 per hour. Write a formula for the total cost of hiring the mechanic.

• y = 15x + 65

• y = 65x + 15

Multiple Choice

To prepare for a recent road trip, Jill filled up her 19-gallon tank. She estimates that her SUV will use about three gallons per hour. Write an equation to model the amount of gasoline, G, remaining in her tank after t hours.

• G=19 – 3t

• G=19 + 3t

• G=3 - 19t

• G=3 + 19t

Multiple Choice

Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.
y=0.5x+10
What does the slope of the graph of this equation represent?

• The daily fee for the moving truck

• The per-mile fee for the moving truck

• How much Charlie paid for the truck

• The number of miles he drove

Multiple Choice

Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.
y=3x+10
What does the y-intercept of the graph of this equation represent?

• The monthly fee

• How much Rich pays per visit

• The number of times Rich goes to the gym

• The total cost at the end of the month

Multiple Choice

A plant is 5cm tall and growing at a rate of 3cm a month.

• y = 5 - 3x

• y = 5x + 3

• y = 3x +5

Multiple Choice

What does the slope represent in this context?

• The number of eggs that fit in the basket

• The mass per egg

• The mass of the basket

• Amount of eggs per basket

Multiple Choice

What does the y-intercept represent in this context?

• The height of the screw head above the wood before Tanvir rotated the screwdriver

• The number of millimeters per rotation that the screw height changes

• The number of rotations it takes to change the screw head height by 111 millimeter

• The number of rotations it takes to get the screw into the wood.

Multiple Choice

What does the y-intercept represent?

• $40 lost buying candy

• 40 weeks of losing money by buying candy

• $40 in the saving account when he started buying candy

• $2 lost per week from savings to buy candy

Multiple Choice

What does the slope represent in this situation?

• $40 per week spent on candy

• $1 spent every 2 weeks on buying candy

• $40 he started with before buying candy

• $2 spent per week to buy candy

Write Linear Equations from Table

Multiple Choice

Which equation matches the table?

• y = x 

• y = 5x

• y = x - 4

• y = x + 4

Multiple Choice

Which equation matches the table?

• y = 3x + 9

• y = 1/3x + 9

• y = x + 3

• y = 12x - 3

Multiple Choice

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

• y = -3x - 10

• y = -1/3x - 10

• y = 3x + 10

• y = 3x - 10

Multiple Choice

What is the equation of the linear function?

• y = -3x + 10
• y = -3x + 16
• y = 3x + 10
• y = 3x + 16

Multiple Choice

What is the equation for the table?

• y =1/4x -3
• y =4x - 3
• y = -3x -3 
• y =-2x -3 

Multiple Choice

What is the Y - INTERCEPT from the table?

• 1

• -5

• 5

• 5/6

MGSE8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Multiple Choice

Two linear functions are shown below. Which function has the greater rate of change?

• Function A

• Function B

Multiple Choice

Two linear functions are shown below. Which function has the greater initial value?

• Function A

• Function B

Multiple Choice

Two linear functions are shown below. Which function has the greater rate of change?

• Function A

• Function B

Multiple Choice

The function y=4x+3 describes Player A's scores in a game of trivia, where x is the number of questions answered correctly and y is the score. The function represented in the table shows Player B's scores. Who earns more points per question?

• Player A

• Player B

Open Ended

Two athletes are training over a two-week period to increase the number of push-ups each can do. Athlete A can do 16 pushups to start, and increases his total by 2 each day. Athlete B's progress is charted in the table. Compare the initial values.

Finding the Rate of Change (Slope)

Multiple Choice

Which equation has the greatest rate of change?

• y = 10x - 5

• y = -3x + 8

• y = -26x

• y = 2x + 14

Multiple Choice

Who is going faster based on their rate of change?

• The Hare

• The Tortoise

Which Function has a lower rate of change?

Multiple Choice

Who has the greater rate of change?

• Hunter has the greater rate of change.

• Casey has the greater rate of change

• They have the same rate of change

Multiple Choice

Which function has the greatest RATE OF CHANGE?

Multiple Choice

Janet is planning her sweet sixteen birthday party. She must decide which party coordinator she should use so that she spends the least amount of money possible. Each coordinator charges an initial fee for their services, plus an additional fee depending on the number of guests that attend the party. Each coordinator's rates are shown in the image.

Which coordinator charges the greatest fee per guest?

• Coordinator A

• Coordinator B

• Coordinator C

• Coordinator D

Multiple Choice

What is the initial value of the following graph?

• (3, 0)
• (0, 3)
• (4, 0)
• (0, 4)

Multiple Choice

Write an equation for the table.

• y = 0.4x

• y = 025x

• y = 4x

• y = 0.04x

MGSE8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally

Multiple Choice

Is this graph linear or nonlinear?

• Linear

• nonlinear

Multiple Choice

What type of slope does the following graph have?

• Postive/Increasing

• Negative/Decreasing

• Zero Slope

• Undefined

Multiple Choice

What is the slope in the picture?

• Positive/Increasing

• Negative/Decreasing

• Zero

• Undefined

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the function linear or nonlinear?

• Linear Function
• Nonlinear Function

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Between which seconds is the line INCREASING?

• Between 7 and 12 seconds
• Between 0 and 1 seconds
• Between 1 and 5 seconds
• Between 12 and 13.5 seconds

Multiple Choice

Which graph is linear?

• Graph A
• Graph B
• Graph C
• Graph D

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Choice

Is this graph a function?

• No

• Yes

Multiple Choice

Is the following an increasing or decreasing function?

• increasing

• decreasing

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Determine if the graph is linear or nonlinear.

• Linear
• Nonlinear

MGSE8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally

Multiple Choice

The graph shows Timmy's distance he is as he leaves school one afternoon. What happens in section B?

• Timmy is walking back to school because he forgot his math book.

• Timmy is talking to a friend and not walking.

• Timmy is walking faster home.

• Timmy is dancing in the street.

Multiple Choice

The graph shows Timmy's distance he is as he leaves school one afternoon. What happens in section C? Why is the distance from school decreasing?

• Timmy is walking back to school because he forgot his math book.

• Timmy is talking to a friend and not walking.

• Timmy is walking faster home.

• Timmy is dancing in the street.

Multiple Choice

The graph shows the speed of Mr. Sam driving to work. Which section shows Mr. Sam stopped in traffic?

• a.

• b.

• g.

• d.

• f.

Multiple Choice

• F
• G
• H
• J

Multiple Choice

• F
• H
• G
• I

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• F
• G
• H
• I

Multiple Choice

Interval 2 is...

• Increasing, linear

• Increasing, nonlinear

• Decreasing, linear

• Decreasing, nonlinear

Multiple Choice

Which intervals are constant?

• 1 and 5

• 2 and 3

• 4 and 6

Multiple Choice

Which intervals are linear?

• 2 and 3

• 4 and 6

Multiple Choice

Is the pattern increasing or decreasing?

• Increasing

• Decreasing

Multiple Choice

Is the pattern linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Select Figure 4 below.

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Select

Which of the following terms describes the function?

• linear

• nonlinear

• discrete

• continuous

• increasing and decreasing

Multiple Choice

On what interval is the function increasing?

• x > 0

• x < 0

• -7 < x < 7

• the function does not increase

Multiple Select

Which of the following words describes the function?

• linear

• nonlinear

• increasing

• decreasing

• increasing and decreasing

Multiple Choice

On what interval is the function decreasing?

• x > 5

• x < 5

• 2.7 < x < 7.3

• y < 5

Multiple Choice

On what interval is the function increasing?

• x < 1

• 1 < x < 3

• 3 < x < 5

• 5 < x < 10

Multiple Choice

On what interval is the function constant?

• x < 1

• 1 < x < 3

• 3 < x < 5

• 5 < x < 10

Multiple Choice

Is the table linear or nonlinear, and why?

• linear, x and y go up evenly

• linear, the numbers go up

• nonlinear, they go up by different amounts

• nonlinear, the ratios aren't equal

Multiple Choice

Is the table linear or nonlinear, and why?

• linear, x and y go up evenly

• linear, the numbers go up

• nonlinear, they go up by different amounts

• nonlinear, the ratios aren't equal

Multiple Choice

Is the table linear or nonlinear, and why?

• linear, x and y go up evenly

• linear, the numbers go up

• nonlinear, they go up by different amounts

• nonlinear, the ratios aren't equal