Tues, 11/8

SWBAT…compute slope Agenda

1. WU (15 min)

2. Notes on slope (30 min)

Warm-Up:

1. Do HW #4 – problems #1 – 4

(interpreting x-and y-intercepts)

HW #5: Slopes of lines (front & back)

Swimming Pool x-int: (14, 0): After 14 hours, the water has a

volume of 0 gallons, or the pool is completely drained.

y-int: (0, 10,080): The pool contained 10,080 gallons of water at time 0, or before it started to drain.

Ewa x-int: (8, 0): It took Ewa 8 minutes to get

home. y-int: (0, 4): Ewa was initially 4 miles from

home.

Temperature x-int: (2, 0): After 2 minutes, the temperature

is 0 degrees F. y-int: (0, -3): At time 0, the temperature is -3

degrees F.

Scuba Diver x-int: (12, 0): After 12 seconds the scuba

diver is at a depth of 0 or at the surface. y-int: (0, -24): At time 0, the scuba diver is

at a depth of -24 meters, or 24 meters below sea level.

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

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

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

• Is the slope positive or negative?

Answer:

Negative, read from left to right

““Official” Definition of SlopeOfficial” Definition of Slope

Slope 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

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.

1

2m

What the graph looks like

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

x y

0 2

2 1

4 0

6 -1

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.

 

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