mth 091 section 13.1 the rectangular coordinate system section 13.2 graphing linear equations
TRANSCRIPT
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MTH 091
Section 13.1The Rectangular Coordinate System
Section 13.2Graphing Linear Equations
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It might be time to invest in some graph paper…
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Plot The Following Points
• P = (-4, -2)• Q = (-3, 2)• R = (3, -5)• S = (5, 3)• T = (-6, 0)• U = (0, 3)
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Name The Following Points
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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.
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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.
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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.
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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
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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, _____ )
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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.