mth 091 section 13.1 the rectangular coordinate system section 13.2 graphing linear equations
TRANSCRIPT
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.