Wed, 12/3

SWBAT…compute slope Agenda

1. WU (5 min)

2. Notes on slope (35 min)

Warm-Up:

1. Set up your notes. Topic is “Slope”

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

How do engineers build bridges?How do engineers build bridges?

How do engineers build roads?How do engineers build roads?

How do builders build roofs?How do builders build roofs?

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

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

• Remember than any percent is a part of 100.

77%

100

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

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

• To find the slope, use the formula

4

4

risem

run (elevacion)

(desplazamiento)

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

• To find the slope, use the formula

4

441

4m

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

• Find the slope of the following lines:

3

2m

1

2A) B)

2

3

risem

run

1

2m

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

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

• Is the slope positive or negative?

Answer:

Positive, read from left to right

1

2m

3

4m

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

• The last 2 lines had a positive slope, let’s look at slopes with negative slopes

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

• We still use rise over run, except the “stairs” are underneath the line.

3

-2

2

3m

1

4m

5

6m

Your turnYour turn

““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

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 (don’t forget arrows)).Connect the line (don’t forget arrows)).

1

2m

What the graph looks like

Find the rate of change:Find the rate of change:

x y

0 2

2 1

4 0

6 -1

 

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

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

Practice ProblemPractice Problem

A horizontal lines passes through (2, 5). What other point does the line contain?

1. (2,3)

2. (0,5)

3. (5,10)

4. (0,2)