Math 0861
Learning Centre
Graphing Linear Equations
A simple way to graph linear equations is to find any two points that satisfy the equation
and then draw a straight line through them.
Consider these sets of similar linear equations:
Example 1: y = x, y = 2x, y = 3x, y = 4x
y
Solution:
y=x
x y
0 0
1 1
y = 2x
x y
0 0
1 2
y = 3x
x y
0 0
1 3
y = 4x
x y
0 0
1 4
y = 4x
y = 3x
y = 2x
5
y=x
-5
5
x
-5
Example 2: y = x, y = x + 1, y = x + 2, y = x + 3
Solution:
y=x
x y
0 0
1 1
y=x+1
x y
0 1
1 2
y=x+2
x y
0 2
1 3
y=x+3
x y
0 3
1 4
y
y=x+1
y=x+2
y=x
y=x+3
5
-5
5
x
Note that these lines are all parallel.
-5
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
Authoredby
byEmily
Gordon
Wong
Simpson
Example 3: y = 3x − 6, y = 3x − 3, y = 3x, y = 3x + 3
Solution:
y = 3x − 6
x y
0 -6
1 -3
y = 3x − 3
x y
0 -3
1 0
y = 3x
x y
0 0
1 3
y = 3x + 3
x y
0 3
1 6
y
y = 3x + 3
y = 3x
y = 3x − 3
5
y = 3x − 6
-5
EXERCISES
5
x
5
x
5
x
-5
A. Graph:
y
1)
y=x−3
x
y
0 −3
1 −2
−1
2
5
-5
2)
3)
4)
y = −x
x
y
0 0
1 −1
−1
2
-5
y
y = 3x + 5
x
y
0
1
−1
−2
y = ½x − 4
x
y
0
2
4
−2
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
5
-5
-5
2
y
5)
y = −2x + 3
x
y
0
1
2
−1
5
-5
6)
y = −¼x − 1
x
y
0
2
4
−4
5
x
5
x
5
x
-5
y
7)
3x + y = 7
x
y
0
1
−1
−2
5
-5
8)
y − 2x = −2
x
y
0
2
4
−2
-5
y
9)
3y = 3x − 2
x y
5
-5
10)
3y = 4
x y
-5
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
3
SOLUTIONS
y
y
2
5
3
y
5
5
5
1
-5
5
x
-5
5
x
-5
5
6
-5
-5
4
-5
y
y
7
5
5
8
9
10
-5
5
x
-5
© 2013 Vancouver Community College Learning Centre.
Student review only. May not be reproduced for classes.
-5
5
x
-5
4
x