MPM1D
1.
2.
Consider the relation y = 2x – 3.
a)
Make a table of values for x-values from 0 to 5.
b)
Graph the relation.
c)
Classify the relation as linear or non-linear.
d)
Add a third column to the table in part a). Label the column “First Differences.” Find the
differences between consecutive y-values and record them in this column.
1
Consider the relation y = 2 x2.
a)
b)
c)
d)
3.
4.
Make a table of values for x-values from 0 to 5.
Graph the relation.
Classify the relation as linear or non-linear.
Find the differences between consecutive y-values. Add a column to your table in part a)
to record the first differences.
Refer to your answers to questions 1 and 2. How can you use first differences to tell if a relation
is linear or non-linear?
Complete each table. State whether each relation is linear or non-linear.
a) x
y
First Differences
0
8
1
10
2
13
3
17
b) x
0
1
2
3
5.
Slope Review and First Differences Worksheet
y
2
6
10
14
First Differences
Complete the table for each equation. Identify each relation as linear or non-linear.
x
y
First Differences
1
2
3
4
a)
c)
y = 2x
y=x+1
b)
d)
y = –3x
y = x2 + 1
Answers are on Ms. Kueh’s Website lkueh.wordpress.com
Answers
1.
a, d)
x
0
1
2
3
4
5
c)
2.
a, d)
x
0
1
2
3
4
5
c)
3.
4.
b)
y
3
1
1
3
5
7
First Differences
2
2
2
2
2
linear
b)
y
First Differences
0
0.5
2
4.5
8
12.5
0.5
1.5
2.5
3.5
4.5
non-linear
If the first differences are equal, the relation is linear. If the first differences are not equal, the
relation is non-linear.
a)
x
y
First Differences
0
8
1
10
2
2
13
3
3
17
4
non-linear
b)
x
y
First Differences
0
2
1
6
4
2
10
4
3
14
4
linear
5.
a)
x
1
2
3
4
b)
x
1
2
3
4
c)
x
1
2
3
4
d)
x
1
2
3
4
y
2
4
8
16
non-linear
First Differences
y
3
6
9
12
linear
First Differences
y
2
3
4
5
linear
First Differences
y
2
5
10
17
non-linear
First Differences
2
4
8
3
3
3
1
1
1
3
5
7