# Simplify. Exercise 4 − 2 5 − 2 2323 2323. Simplify. 5 − 2 4 − 2 3232 3232 Exercise.

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Simplify. Exercise 4 − 2 5 − 2 2323 2323

Simplify. 5 − 2 4 − 2 3232 3232 Exercise

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

Simplify. 2 − 4 2 − 5 2323 2323 Exercise

Simplify. 2 − 2 5 − 2 0 0 Exercise

Simplify. 4 − 2 2 − 2 undefined Exercise

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

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

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

y y x x

y y x x

up to rightpositive down to rightnegative horizontalzero verticalundefined Slope

Slope = m = rise run

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

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

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

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

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

y y x x (−1, 2) (3, 2)

= = 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

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

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

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

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

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

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

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

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

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

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

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

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

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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