Linear vs. Non-Linear
For each equation, fill in the table and graph the points. You can graph all 4 equations on the
coordinate plane below. Number each graph. Circle the equations that produce a linear graph.
1. y = 2x + 3
x
y
3. y = y = x - 4
x
y
2. y = x2 – 3x
x
y
1
4. y = x
3
x
y
What do you notice about the equations that produce a linear graph? How are they different from
an equation that produces a non-linear graph?
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13. Paloma looks at the table below and believes it is a linear function. Rebeca disagrees and
thinks it is a non-linear function. Who do you agree with? Why?
x
y
0
0
1
2
2
8
3
18
4
32
5
50
6
72
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14. Matias looks at the table below and believes it is a linear function. Arjun disagrees and thinks
it is a non-linear function. Who do you agree with? Why?
x
y
0
5
1
7
2
9
3
11
4
13
5
15
6
17
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15. Give an example of a table that represents a linear function.
x
y
16. Give an example of a table that represents a non-linear function.
x
y
17. Laila pays $20 each month to join an afterschool club. If Laila made a graph of the amount of
money she has spent from September to June, would the graph be linear? Why or why not?
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Linear vs. Non-Linear - Answers
For each equation, fill in the table and graph the points. You can graph all 4 equations on the
coordinate plane below. Number each graph. Circle the equations that produce a linear graph.
1. y = 2x + 3
x
y
-1
1
0
3
Red
1
5
2. y = x2 – 3x Blue
2
7
3
9
4 5
11 13
4
0
5
1
8
2
13
3
-1
4
1
4. y = x
3
3. y = y = x - 4 Purple
x
y
x
y
18
4
29
5
40
6
x
y
-6
-2
0
0
1
-2
2
-2
3
0
4
4
5
10
Green
-3
-1
0
0
3
1
6
2
9
3
12
4
What do you notice about the equations that produce a linear graph? How are they different from
an equation that produces a non-linear graph?
The linear graphs all have an equation with an x that is to the first power. The square root
equation made a curve and so did the equation with an x2.
13. Paloma looks at the table below and believes it is a linear function. Rebeca disagrees and
thinks it is a non-linear function. Who do you agree with? Why?
x
y
0
0
1
2
2
8
3
18
4
32
5
50
6
72
I agree with Rebeca. The points to do lie on a line. The y values are not increasing at the same rate
even though the x values are increasing by one.
14. Matias looks at the table below and believes it is a linear function. Arjun disagrees and thinks
it is a non-linear function. Who do you agree with? Why?
x
y
0
5
1
7
2
9
3
11
4
13
5
15
6
17
I agree with Matias. The x values are increasing by one, while the y values are increasing by 2.
When graphed, these points would be linear.
15. Give an example of a table that represents a linear function.
x
y
Answers will vary.
16. Give an example of a table that represents a non-linear function.
x
y
Answers will vary.
17. Laila pays $20 each month to join an afterschool club. If Laila made a graph of the amount of
money she has spent from September to June, would the graph be linear? Why or why not?
Yes, the graph would be linear. The number of months (input) is increasing by one, while the
amount of money spent (output) is increasing by the same amount ($20). When the rate of change
is constant, the graph is linear.