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?

Suppose you were asked to graph the solution set of the linear equation,

.3 yx You could start by creating a table of

values.

xy

Choose any number to use as x or y . . .

3 yx

xy

0

3 y

. . . and substitute the number for the variable.

3

0x

3y

xy

0

Then calculate to find,

3 y

Continue, until you have 3 sets of x and y values.

3

3x

xy

0 30

3x

Continue, until you have 3 sets of x and y values.

3xy

0 30

y

63

6

With your table completed for three sets of values, you are ready to graph the line.

3xy

0 30 6

3

3 yx

When x is 0, y is 3, so plot the point, (0, 3).

3xy

0 30 6

3

3 yx 3,0

And when x is 3, y is 0, so plot the point, (3, 0).

3xy

0 30 6

3

3 yx

0,3

And finally, when x is -3, y is 6, so plot the point, (-3, 6).

3xy

0 30 6

3

3 yx 6,3

If the three points do not line up, you need to find your mistake.

3xy

0 30 6

3

3 yx

If they do line up, you just need to connect the dots.

This is the graph of the linear equation, .3 yx

Create a table of values for each equation, and graph it on grid paper:

1.

2.

3.

5 yx

72 yx

42 xy

4. 121 xy