1. Comparing Functions Represented in Different ways
Graphs vs. Equations vs. Tables vs. Verbal Descriptions
Look at the problem
Complete the following for each problem:
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions
Click to see the answers
Follow prompts to see explanations

2. Compare the functions represented in different ways1.
Compare the functions represented in different ways
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions x y 2 1 4 6 3 8
Write down your answers, then click anywhere on the screen to check them. A B
Both functions are linear
Click on each of the answers to see explanations
Steeper slope
Greater y-intercept

3. Compare the functions represented in different ways1.
Compare the functions represented in different ways
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions x y 2 1 4 6 3 8
Write down your answers, then click anywhere on the screen to check them. A B
Both functions are linear
Click on each of the answers to see explanations
Steeper slope
Greater y-intercept
Once you completely understand #1, click here to move onto #2.

4. To determine the slopes, graph both functions
(x,y) x y 2 1 4 6 3 8
(0,2)
(1,4)
(2,6)
(3,8) B A
Click here for another strategy to compare slope
B increases faster, or has a steeper slope
*Think: it would be harder to walk up B if it was a mountain, than A. B is steeper.

5. Or, make them both into tables to determine the slopes
Change in y
Slope =
Change in x x y x y 2 1 4 6 3 8 4 4 -1 2 -1 1 3 3 -1 2 -1 1 2 2 -1 2 -1 1 1 1 -1 2
= 1
= 2
Slope of A=
Slope of B = 1 -1
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B has a greater (or steeper) slope

6. To determine if they are linear, graph both functions
(x,y) x y 2 1 4 6 3 8
(0,2)
(1,4)
(2,6)
(3,8) B A
Click here for another strategy to determine if a function is linear or nonlinear.
Linear = straight line
They are both linear.

7. Or, make them both into tables to determine if they are linear.
If x and y both change by a constant rate, the function is linear. x y x y 2 1 4 6 3 8 4 4 -1 2 -1 1 3 3 -1 2 -1 1 2 2 -1 2 -1 1 1 1
Constant rate of change
Constant rate of change
Constant rate of change
Constant rate of change
linear
linear
Both A and B are linear functions.
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8. To find the y-intercepts, graph the functions
y-intercept is where the line crosses (or intersects) the y-axis.
(x,y) x y 2 1 4 6 3 8
(0,2)
Intersects y-axis at 2
(1,4)
Intersects y-axis at 0
(2,6)
(3,8) B A
Click here for another strategy to compare y-intercepts
B has the greater y-intercept
*B intersects the y-axis at a greater number than A

9. Or, make them both into tables to determine the y-intercepts
When x = 0, the value for y tells you the y-intercept. B A x y x y 2 1 4 6 3 8 4 4 3 3
When x = 0
y = 2 2 2 1 1
The y-intercept for B is 2.
When x = 0
y = 0
The y-intercept for A is 0.
B has a greater y-intercept (or the line intersects the y-axis at a greater number for function B than it does for function A).
Click here to go back to the original problem

10. Compare the functions represented in different ways2.
Compare the functions represented in different ways D
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions 8 x y 2 3 4 6 5 C
y = 3x +4
Write down your answers, then click anywhere on the screen to check them.
Click on each answer to see the explanations
C has a greater y-intercept than D
C is linear; D is nonlinear
C has a slope of 3; D does not have a slope because it is nonlinear

11. Compare the functions represented in different ways2.
Compare the functions represented in different ways D
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions 8 x y 2 3 4 6 5 C
y = 3x +4
Write down your answers, then click anywhere on the screen to check them.
Click on each answer to see the explanations
C has a greater y-intercept than D
C is linear; D is nonlinear
C has a slope of 3; D does not have a slope because it is nonlinear
Once you completely understand #2, click here to move onto #3.

12. D C Linear or Nonlinear? y = mx + b y = 3x +48 x y 2 3 4 6 5
Equations in this form
(slope-intercept form)
are always linear 3 2 2 1 2 1 C
y = 3x +4 2 1
Not a constant rate of change
Constant rate of change
nonlinear
C is linear; D is nonlinear
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13. D C Compare the slopes y = mx + b y = 3x +4 C has a slope of 3;8 x y 2 3 4 6 5
m = slope 3 2 2 1 2 1 C
y = 3x +4 2 1
Not a constant rate of change
Constant rate of change
slope = 3
nonlinear
C has a slope of 3;
D does not have a slope because it is nonlinear
No slope
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14. D C Compare the y-intercepts y = mx + b y = 3x +4
y-intercept = the y value when x = 0 8 x y 2 3 4 6 5
y = 0
b = y-intercept
when x = 0 D C
y = 3x +4
y-intercept = 0
y-intercept = 4
C has a greater y-intercept than D
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15. Compare the functions represented
in different ways 3. E F
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions
y = -2x
Write down your answers, then click anywhere on the screen to check them.
Click on the answers to see the explanations
E and F are both linear
E and F have the same slope
E has a greater y-intercept than F

16. Compare the functions represented
in different ways 3. E F
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions
y = -2x
Write down your answers, then click anywhere on the screen to check them.
Click on the answers to see the explanations
E and F are both linear
E and F have the same slope
E has a greater y-intercept than F
Once you completely understand #3, click here to move onto #4.

17. y = -2x + 0 F E Linear or Nonlinear? y = mx + b
Equations in this form
(slope-intercept form)
are always linear E
y = -2x
+ 0
Linear
The graph is a straight line, so it is linear.
E and F are both linear
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18. y = -2x + 0 E F Compare the slopes y = mx + b
Change in y (rise) = -2
Change in x (run) = 1
slope = -2
y = mx + b F
m = slope
y = -2x
+ 0
slope = -2
E and F have equal slopes
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19. y = -2x + 0 E F Compare the y-intercepts y = mx + b
b = y-intercept
y = -2x
+ 0
Intersects y-axis at -2
y-intercept = 0
y-intercept = -2
E has a greater y-intercept than F
Click here to go back to the original problem

20. Compare the functions represented in different ways4
Compare the functions represented in different ways G
Maggie puts $5 in the bank every week. H 4 x y 1 2 8 3 12 16
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions
Write down your answers, then click anywhere on the screen to check them.
Click on the answers to see the explanations
G and H are both linear.
G and H have the same y-intercept.
G has a greater slope.

21. Compare the functions represented in different ways4
Compare the functions represented in different ways G
Maggie puts $5 in the bank every week. H 4 x y 1 2 8 3 12 16
Determine if the functions are linear or nonlinear
Compare the slopes of the functions
Compare the y-intercepts of the functions
Write down your answers, then click anywhere on the screen to check them.
Click on the answers to see the explanations
G and H are both linear.
G and H have the same y-intercept.
G has a greater slope.
Once you completely understand #4, click here to move on.

22. G H Maggie puts $5 in the bank every week. Linear or Nonlinear?4 x y 1 2 8 3 12 16 H 1 4
y = mx + b 1 4
Equations in this form
(slope-intercept form)
are always linear 1 4
1. Define the variables 1 4
y = total amount of $ in the bank
Constant rate of change
Constant rate of change
x = # of weeks
2. Write the equation
Linear
y = x 5
+ 0
are put in each week
Linear
Since G has a constant rate of change (5 more dollars each week) and so does H, they are both linear
to equal the total amount in the bank?
How many dollars
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23. G H Compare the slopes Maggie puts $5 in the bank every week.4 x y 1 2 8 3 12 16 H 1 4
y = mx + b 1 4
m = slope 1 4
1. Define the variables 1 4
y = total amount of $ in the bank
x = # of weeks 4
Change in y
2. Write the equation
Slope = = = 4 1
Change in x
y = x 5
+ 0
are put in each week
G has a greater slope than H
to equal the total amount in the bank?
How many dollars
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slope = 5

24. G H Compare the y-intercepts Maggie puts $5 in the bank every week.4 x y 1 2 8 3 12 16
y = 0 H
when x = 0
y = mx + b
b = y-intercept
1. Define the variables
y = total amount of $ in the bank
x = # of weeks
2. Write the equation
y-intercept = 0
y = x 5
+ 0
are put in each week
y – intercepts are equal
to equal the total amount in the bank?
How many dollars
y-intercept = 0
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25. Great work!
Now, move on to _________