4 minutes Warm-Up Graph. 5x – 4y = 20 2) x = 5 3) y = -2.

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Presentation transcript:

4 minutes Warm-Up Graph. 5x – 4y = 20 2) x = 5 3) y = -2

5.1 Slope Objectives: To find the slope of a line given two points on the line To describe slope for horizontal and vertical lines

Slope -4 -2 2 4 6 8 10 -6 -8 -10 Slope = run rise

Example 1 Graph the line containing points (2,1) and (7,6) and find the slope. -4 -2 2 4 6 8 10 -6 -8 -10 Slope = run rise

Practice Graph the line containing these points and find their slopes. 1) (-2,3) (3,5) 2) (0,-3) (-3,2)

Slope Slope = or

Example 2 Find the slope of the line containing points (1,6) and (5,4).

Practice Find the slope of the lines containing these points. 1) (2,2) (8,9) 2) (-2,3) (2,1) 3) (5,-11) (-9,4)

Slope of a Horizontal Line What about the slope of a horizontal line? -4 -2 2 4 6 8 10 -6 -8 -10 What is the rise? What is the run? 6 Slope = The slope of ANY horizontal line is 0.

Slope of a Vertical Line What about the slope of a vertical line? -4 -2 2 4 6 8 10 -6 -8 -10 What is the rise? 5 What is the run? Slope = The slope of ANY vertical line is undefined.

Example 1 Find the slope of the line y = -4. Slope = -4 -2 2 4 6 8 10 -6 -8 -10 Slope =

Example 2 Find the slope of the line x = 7. Slope = -4 -2 2 4 6 8 10 -6 -8 -10 Slope = The line has no slope.

Practice Find the slopes, if they exist, of the lines containing these points. 1) (9,7) (3,7) 2) (4,-6) (4,0) 3) (2,4) (-1,5)

5 minutes Warm-Up Graph. Then find the slope. y = 3x + 2 2) y = -2x +5

5.2 Equations and Slope Objectives: To find the slope and y-intercept of a line from an equation

Slope-Intercept Equation Find the slope of the line y = 2x - 4. 8 y = 2x - 4 6 4 x y 2 -4 -8 -6 -4 -2 2 4 6 8 1 -2 -2 rise: -4 2 -4 run: -2 -6 -8 The y-intercept is -4.

Slope-Intercept Equation y = mx + b y = 4x + 8 slope y = 2x - 3 y-intercept slope = 4 y-intercept = 8 slope = 2 y-intercept = -3

Example 1 Find the slope and y-intercept of the line y = -4x + 4. The slope is -4. The y-intercept is 4.

Example 2 Find the slope and y-intercept of the line y = 5x - 7. The slope is 5. The y-intercept is -7.

Practice Find the slope and y-intercept of each line. y = x + 3

Example 3 Find the slope and y-intercept of the line 3x + 4y = 12. solve for y -3x -3x 4y = 12 – 3x 4 4 slope y-intercept = 3

Practice Find the slope and y-intercept of each line. y = -x - 3 2) 8x + 2y = 10 3) 3y – 6x = 12

Homework p.326 #1-10,19-27 odds

Warm-Up 4 minutes Find the slope and y-intercept. y = 3x + 4 3) 2x + 7y = 9 4) 4x = 9y + 7

Example 1 Graph y = 3x + 2. What is the slope of this line? 8 What is the slope of this line? 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 What is the y-intercept? -4 b = 2 -6 -8

Example 2 Graph What is the slope of this line? 8 What is the slope of this line? 6 4 2 -8 -6 -4 -2 2 4 6 8 -2 What is the y-intercept? -4 b = -3 -6 -8

Practice Graph each line. y = 3x - 5 2) y = -2x + 4 3)

Example 3 Graph 3x + 4y = 12. 3x + 4y = 12 solve for y -3x -3x

Example 3 Graph 3x + 4y = 12. slope y-intercept 8 6 4 2 -8 -6 -4 -2 2

Practice Graph each line. 7x + 2y = 4 2) 5y – 10 = 4x