WARM UP SCHOOL BAKE SALE (Lesson 3.5) You have one hour to make cookies for your school bake sale. You spend 24 minutes mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, which model can you use to find how many trays you can bake during the hour? a.x( ) = 60 b.12x + 24 = 60 4
WARM UP SCHOOL BAKE SALE (Lesson 3.5) You have one hour to make cookies for your school bake sale. You spend 24 minutes mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, which model can you use to find how many trays you can bake during the hour? a.x( ) = 60 b.12x + 24 = 60 3
WARM UP SCHOOL BAKE SALE (Lesson 3.5) You have one hour to make cookies for your school bake sale. You spend 24 minutes mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, which model can you use to find how many trays you can bake during the hour? a.x( ) = 60 b.12x + 24 = 60 2
WARM UP SCHOOL BAKE SALE (Lesson 3.5) You have one hour to make cookies for your school bake sale. You spend 24 minutes mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, which model can you use to find how many trays you can bake during the hour? a.x( ) = 60 b.12x + 24 = 60 1
WARM UP SCHOOL BAKE SALE (Lesson 3.5) You have one hour to make cookies for your school bake sale. You spend 24 minutes mixing the dough. It then takes 12 minutes to bake each tray of cookies. If you bake one tray at a time, which model can you use to find how many trays you can bake during the hour? a.x( ) = 60 b.12x + 24 = 60 0
4.5 The Slope of a Line You can describe steepness by a ratio called slope. To find the slope, divide the rise by the run. Slope = = = = 2 Vertical rise Horizontal run Vertical Rise = 10 Horizontal run = 5
4.5 The Slope of a Line EXAMPLE 1 The Slope Ratio: Find the slope of a hill that has a vertical rise of 40 feet and a horizontal run of 200 feet. Let m represent slope. SOLUTION m = = = ANSWER> the slope of the hill is Vertical rise Horizontal run Vertical Rise = 40 ft. Horizontal run = 200 ft. 1515
4.5 The Slope of a Line The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line. Notice how you can subtract coordinates to find the rise and the run. Slope = = = rise run 2525 (3,2) (8,4) Rise = 4 -2 = 2 Run = 8 -3 = 5
SLOPE When you use the formula for slope, you can label either point as (x 1,y 1 ) and the other as (x 2,y 2 ). After labeling the points, you must subtract the coordinates in the same order in both the numerator and the denominator. THE SLOPE OF A LINE The slope m of a line that passes through points (x 1,y 1 ) and (x 2,y 2 ) is m = = = y 1 – y 2 x 1 – x 2 Change in y Change in x rise run
4.5 The Slope of a Line EXAMPLE 2 Positive Slope Find the slope of the line that passes through the points (1,0) and (3,4). SOLUTION STEP ONE m = STEP TWO = Substitute values STEP THREE = Simplify STEP FOUR = 2 Slope is positive ANSWER> The slope of the line is y 1 – y 2 x 1 – x 2 Subtract y-values Subtract x-values (1,0) (3,4)
4.5 The Slope of a Line CHECK POINT Find a Positive Slope Find the slope of the line that passes through the two points 1.(x 1,y 1 ) = (3,5) and (x 2,y 2 ) = (1,4) 2.(x 1,y 1 ) = (2,0) and (x 2,y 2 ) = (4,3) 3.(x 1,y 1 ) = (2,7) and (x 2,y 2 ) = (1,3)
4.5 The Slope of a Line EXAMPLE 3 Negative Slope Find the slope of the line that passes through the points (0,3) and (6,1). SOLUTION STEP ONE m = STEP TWO = Substitute values STEP THREE = = Simplify STEP FOUR = Slope is negative ANSWER> The slope is y 1 – y 2 x 1 – x 2 Subtract y-values Subtract x-values (0,3) (6,1) 3 3 3
4.5 The Slope of a Line CHECK POINT Find a Negative Slope Find the slope of the line that passes through the two points 1.(x 1,y 1 ) = (2,4) and (x 2,y 2 ) = (-1,5) 2.(x 1,y 1 ) = (0,9) and (x 2,y 2 ) = (4,7) 3.(x 1,y 1 ) = (-2,1) and (x 2,y 2 ) = (1,-3) YOU’RE CERTIFIED
4.5 The Slope of a Line CLASSWORK/HOMEWORK Page 233 #s