A linear equation is defined as an equation whose graph forms a line, characterized by variables raised only to the first power. To graph a linear equation, one can create a table of values by choosing numbers for x or y, substituting them into the equation, and calculating the corresponding values. Once three sets of values are obtained, the points can be plotted and connected to form the line representing the equation.

2. Linear Equation: an equation whose
graph forms a line.
1143 =− yx
262
+−= xxy
is linear.
is not.
In linear equations, all variables are
taken to the first power.
Linear means of a
line. So a linear equation is the equation
of a line.
Why?

3. Suppose you were asked to graph the
solution set of the linear equation,
.3=+ yx
You could start by creating a table of
values.
x
y

4. Choose any number to use as x or y . . .
3=+ yx
x
y
0

5. 3=+ y
. . . and substitute the number for the
variable.
3
0x
3=y
x
y
0
Then calculate to find,

6. 3=+ y
Continue, until you have 3 sets of x and
y values.
3
3x
x
y
0 3
0

7. 3=+x
Continue, until you have 3 sets of x and
y values.
3
x
y
0 3
0
y
6
3−
6

8. With your table completed for three sets
of values, you are ready to graph the
line.
3
x
y
0 3
0 6
3−
3=+ yx

9. When x is 0, y is 3, so plot the point,
(0, 3).
3
x
y
0 3
0 6
3−
3=+ yx ( )3,0

10. And when x is 3, y is 0, so plot the
point, (3, 0).
3
x
y
0 3
0 6
3−
3=+ yx
( )0,3

11. And finally, when x is -3, y is 6, so
plot the point, (-3, 6).
3
x
y
0 3
0 6
3−
3=+ yx ( )6,3−

12. If the three points do not line up, you
need to find your mistake.
3
x
y
0 3
0 6
3−
3=+ yx
If they do line up, you just need to
connect the dots.

13. This is the graph of the linear equation,
.3=+ yx

14. Create a table of values for each
equation, and graph it on grid paper:
1.
2.
3.
5−=− yx
72 =+ yx
42 −= xy
4. 1
2
1
+= xy