mon, 12/3 swbat…compute slope agenda 1. wu (5 min) 2. notes on slope (45 min) warm-up: set up your...

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Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front & back)

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Page 1: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Mon, 12/3

SWBAT…compute slope Agenda

1. WU (5 min)

2. Notes on slope (45 min)

Warm-Up:Set up your notes. Topic is “Slope”

HW#3: Slopes of lines (front & back)

Page 2: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

How can we write 7% as a fraction?How can we write 7% as a fraction?

Page 3: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

7% as a fraction??7% as a fraction??

• Remember than any percent is a part of 100.

77%

100

Page 4: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

The grade or incline of a road is the The grade or incline of a road is the same as slopesame as slope

• Here is the picture:

7 feet

100 feet

Page 5: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Slope of a line (m)Slope of a line (m)

• To find the slope, use the formula

4

4

risem

run (elevacion)

(desplazamiento)

Page 6: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Slope of a line (m)Slope of a line (m)

• To find the slope, use the formula

4

441

4m

Page 7: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Why do we use Why do we use mm for slope? for slope?

• Possibly because m comes from the French word “monter”, which means to climb

Page 8: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Slope of a line (m)Slope of a line (m)

• Is the slope positive or negative?

Answer:

Positive, read from left to right

Page 9: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Slope of a line (m)Slope of a line (m)

• Is the slope positive or negative?

Answer:

Negative, read from left to right

Page 10: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

1

4m

Page 11: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

5

6m

Page 12: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Your turnYour turn

Page 13: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

““Official” Definition of SlopeOfficial” Definition of SlopeSlope is the change in the vertical distance (rise) over the change in the horizontal distance (run)

Pendiente: Razon del cambio en la coordenada y (elevacion) al cambio correspondiente en la coordenada x (desplazamiento) a medida que uno se mueve de un punto a otra en una recta.

12

12

xx

yy

x

y

run

risemslope

12

12

xx

yym

Page 14: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Find the slope of the line that passes Find the slope of the line that passes through (1, 0) and (-1, -1).through (1, 0) and (-1, -1).

Question

(x(x11, y, y11)) (x(x22, y, y22))

(To see the slope visually… Plot these points. (To see the slope visually… Plot these points. Connect the line.Connect the line.

Page 15: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

1

2m

What the graph looks like

Page 16: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

What is the slope of this line?What is the slope of this line?

x y

0 2

2 1

4 0

6 -1

Page 17: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Horizontal lines have a slope of Horizontal lines have a slope of ______ Vertical lines have a slope of Vertical lines have a slope of ______

HorizontalVertical

m = 0

m = undefined

Algebraically prove that the slope of a vertical line is undefined.

Page 18: Mon, 12/3 SWBAT…compute slope Agenda 1. WU (5 min) 2. Notes on slope (45 min) Warm-Up: Set up your notes. Topic is “Slope” HW#3: Slopes of lines (front

Directions: Find the value of r so the line that passes through each pair of points has the given slope.

(12, 10), (-2, r) m = -4

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