3.3 – Slope. Recall how to graph y = 2x – 3. 3.3 – Slope.

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Presentation transcript:

3.3 – Slope

Recall how to graph y = 2x – – Slope

Recall how to graph y = 2x – – Slope

Recall how to graph y = 2x – 3. x 3.3 – Slope

Recall how to graph y = 2x – 3. x – Slope

Recall how to graph y = 2x – 3. x2x – – Slope

Recall how to graph y = 2x – 3. x2x – 3y – Slope

Recall how to graph y = 2x – 3. x2x – 3y(x, y) – Slope

Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

Slope

Slope = Change in y Change in x

Slope = Change in y Change in x m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 )

Slope = Change in y Change in x m = y 2 – y 1, x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4)

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4)

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) (3 – (-1))

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 2 1

Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 2 1

b.

b. Slope =

b. Slope = -1

3

b. Slope = -1 3 c. (1,2) and (-1,2)

b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2

b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1

b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) x 2 – x 1 -1 – 1

b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) = 0 x 2 – x 1 -1 – 1 -2

b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) = 0 = 0 x 2 – x 1 -1 – 1 -2

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year.

***Time is always the independent (x) variable!

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 x 2 – x 1

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 x 2 – x 1

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990)

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) =

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) = = 893

Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) = = 893 = $893/yr.