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