1. MTH 091 Section 13.1 The Rectangular Coordinate System Section 13.2 Graphing Linear Equations

2. It might be time to invest in some graph paper…

3. Plot The Following Points P = (-4, -2) Q = (-3, 2) R = (3, -5) S = (5, 3) T = (-6, 0) U = (0, 3)

4. Name The Following Points

5. 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.

6. 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.

7. 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.

8. 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. xy 0 0 8 xy 0 0 4

9. 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, _____ )

10. 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.