MTH 091

Section 13.1The Rectangular Coordinate System

Section 13.2Graphing Linear Equations

It might be time to invest in some graph paper…

Plot The Following Points

• P = (-4, -2)• Q = (-3, 2)• R = (3, -5)• S = (5, 3)• T = (-6, 0)• U = (0, 3)

Name The Following Points

Linear Equations

• A linear equation in two variables in the form Ax + By = C

• This form of a linear equation is referred to as standard form.

• The graph of every linear equation is a straight line. The line may slant upwards or downwards, or be horizontal or vertical.

The Table of Values Method

1. Make a table with column headings x and y.2. Choose values (usually 3) for either x or y (usually x

but it doesn’t have to be this way).3. Substitute each value into the equation and solve

for the other variable. Do not be concerned if you get a fractional answer.

4. Create an ordered pair (x, y) from the two values.5. Plot these ordered pairs and draw a line through

them.

Examples

1. Complete each ordered pair so that is a solution of the equation y = -4x + 7.

a) (2, _____ )b) ( _____, 0)c) ( _____, -5)

2. Solve 6x + y = 13 for y.

More Examples

3. Complete the table of values for 4x + 5y = 20.

4. Complete the table of values for y = 2x, then graph the equation.

x y

0

0

8

x y

0

0

4

Still More Examples

5. Graph the linear equation 3x – y = 6.

6. Complete the given ordered pairs, and graph the line for x + y = 7; (1, ______ ), ( _____, 2)

7. Complete the given ordered pairs, and graph the line for 4x = -y – 8; ( ____, 0); (-2, _____ )

A Final Word (for now)

• Some of you may have previously used slope-intercept form (y = mx + b) to graph linear equations.

• Hold on: it’s coming. Meanwhile, don’t sleep on the table-of-values method. It can be useful as well.