techmathi - rate of change and slope
TRANSCRIPT
Bell RingerEvaluate each function rule for x = -5.
Write in simplest form:
1.y = x – 7
2. y = (-2/5)x + 3
3. y = 7 - x
4. 7 – 33 – 1
5. -1 – 2 0 – 5
Rate of Change and Slope
Rate of Change
Rate of change = Change in yChange in x
# of days Rental Charge
1 60
2 80
3 100
4 120
5 140It costs $______ per day.
Rate of Change
Rate of change = Change in yChange in x
Miles Fee Charged
100 30
150 42
200 54
250 66
300 78It costs $______ per mile.
You try!
Day Amount Owed
1 135
2 120
3 105
4 90
5 75
After every 1 day, the price decreases by $______.
People Cost
2 7.90
3 11.85
4 15.80
5 19.75
6 23.70
For every 1 person, the price is $______.
1. 2.
The Rate of Change of a line is called its SLOPE.
Slope
rise runSlope = y2 – y1
x2 – x1
=
If you are given two sets of points,
(x1 , y1) and (x2 , y2)
you can find the slope using the formula above.
rise runSlope = y2 – y1
x2 – x1
=
Find the slope of the line through A(-2 , 1) and B(5 , 7)
Find the slope of the line through A(-1 , 3) and B(7 , 9)
Find the slope of the line through A(1 , 2) and B(7 , 4)
Find the slope of the line through A(0 , 5) and B(6 , -7)
Find the slope of the line through A(-2 , 4) and B(0 , -6)
You try!
rise runSlope =
Graph the ordered pair:
(-1 , 0) and (1 , 3)
What is the slope?
rise runSlope =
Graph the ordered pair:
(2 , 2) and (-4 , 6)
What is the slope?
rise runSlope =
Graph the ordered pair:
(0 , -2) and (-1 , 2)
What is the slope?
You try!
Graph the ordered pair:
(-1 , -3) and (1 , 5)
What is the slope?
Slopes of Lines
Horizontal Lines
Find the slope of the line through (1, 2) and (4, 2).
The slope of a horizontal line is always 0.
Slopes of Lines
Vertical Lines
Find the slope of the line through (4, 2) and (4, -1).
The slope of a vertical line is always undefined.
Positive and Negative Slopes
If m > 0, then the line will slant upward from left to right.
If m < 0, then the line will slant downward from left to right.
State whether each line is horizontal, vertical, has a positive slope, or a negative slope.
1. 2. 3. 4.
Homework
WB pg 70 #11-27 All