A solution of an equation is the ordered pair (x, y) that makes the equation true for the two variables x and y.

The set of all points (x, y) that are solutions to the equation is the graph of an equation in x and y.

Drections:

Use a table of values to graph the equation.

Process:

Step 1: Rewrite the equation in function form, if necessary.

Step 2: Choose a few values of x and make a table of values.

Step 3: Plot the points from the table. The graph of the equation is the line through theses points.

Example 1:

Use a table of values to graph the equation y = 2x - 1.

x	2x -1	y	Points
-1	2(-1)-1	-3	(-1, -3)
0	2(0)-1	-1	(0, -1)
1	2(1)-1	1	(1, 1)
2	2(2)-1	3	(2, 3)

Example 2:

Use a table of values to graph the equation 3x + 4y = 8.

First, write in function form.

3x + 4y = 8

4y = -3x + 8

y = -3/4 x + 2

x	-3/4 x + 2	y	Points
-4	-3/4(-4) + 2	5	(-4, 5)
0	-3/4(0) + 2	2	(0, 2)
4	-3/4(4) + 2	-1	(4, -1)
8	-3/4(8) + 2	-4	(8, -4)

 

Special Graphs:

Example 3:

Graph x = -3.

Each value of x is always -3. Choose different values for y in the table.

x	y	Points
-3	0	(-3, 0)
-3	1	(-3, 1)
-3	2	(3, 2)
-3	3	(-3. 3)

Example 4:

Graph y = 2.

Each value of y is always 2. Choose different values for x in the table.

x	y	Points
0	2	(0, 2)
1	2	(1, 2)
2	2	(2, 2)
3	2	(3, 2)

 

Assignment:

Use a table of values to graph each equation.

1. y = x + 1

2. y = -x - 3

3. y = 2x + 1

4. y = -3x + 2

5. 2x - y = 6

6. 3x + 2y = 8

7. x = 4

8. x = -1

9. y = 3

10. y = -2

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