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Simplify. Exercise 4 − 2 5 − 2 2323 2323

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Simplify. 5 − 2 4 − 2 3232 3232 Exercise

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Simplify. 2 − 4 5 − 2 Exercise 2323 2323 – –

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Simplify. 2 − 4 2 − 5 2323 2323 Exercise

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Simplify. 2 − 2 5 − 2 0 0 Exercise

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Simplify. 4 − 2 2 − 2 undefined Exercise

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The rise is the vertical change from point P 1 to point P 2 on a line. Rise

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The run is the horizontal change from point P 1 to point P 2 on a line. Run

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The slope of a line is the ratio of the rise to the run. The variable m is often used for slope. Slope

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y y x x

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y y x x

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up to rightpositive down to rightnegative horizontalzero verticalundefined Slope

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Slope = m = rise run

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y y x x −3 1 1 Find the slope of the given line. m = = −3 −3 1 Example 1

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If a line contains the points P 2 (x 2, y 2 ) and P 1 (x 1, y 1 ), then m = vertical change y 2 − y 1 horizontal change x 2 − x 1 = = Slope Formula

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Find the slope of the line that contains the points (1, 2) and (7, 5). m = = y 2 − y 1 x 2 − x 1 5 − 2 7 − 1 = = 3636 3636 = = 1212 1212 Example 2

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Find the slope of CD passing through (5, 3) and (2, 5). m = = y 2 − y 1 x 2 − x 1 5 − 3 2 − 5 = = 2 −3 = − 2323 2323 Example 3

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Find the slope of EF passing through (3, 2) and (−1, 2). m = = y 2 − y 1 x 2 − x 1 2 − 2 −1 − 3 = = 0 −4 = 0 Example 4

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y y x x (−1, 2) (3, 2)

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= = 4040 4040 Find the slope of the line passing through the points (2, 1) and (2, 5). m = = y 2 − y 1 x 2 − x 1 5 − 1 2 − 2 Example 5

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y y x x (2, 5) (2, 1)

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m = 3 Graph and determine the slope of the following lines. y = 3x + 5 Example

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1212 1212 y = − x + 2 Graph and determine the slope of the following lines. m = − 1212 1212 Example

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2323 2323 y = x − 1 Graph and determine the slope of the following lines. m = 2323 2323 Example

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m = 0 Graph and determine the slope of the following lines. y = 4 Example

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m = −3 Graph and determine the slope of the following lines. y = −3x + 6 Example

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undefined Graph and determine the slope of the following lines. x = 4 Example

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They are the same. Compare the slopes of the lines in the previous questions to the coefficients of x. Example

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m = 5252 5252 Find the slope of the line through (3, 7) and (5, 12). Example

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m = −6 Find the slope of the line through (2, 3) and (4, −9). Example

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m = 0 Find the slope of the line through (2, 5) and (3, 5). Example

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m = undefined Find the slope of the line through (1, 1) and (1, 2). Example

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Their slopes are the same and the lines are parallel. Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2. Example

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Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 3 Equations and Inequalities in Two Variables; Functions.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 3 Equations and Inequalities in Two Variables; Functions.

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