Write down everything you think about/remember about the following terms: 1. slope 2. rate of...
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Write down everything you think about/remember about the following terms:1. slope2. rate of change
5.1 rate of change and slope
I can find rates of change from tables and I can find the slope given two points.
Rate of change: Change in the dependent variableChange in the independent variable
The table shows the distance a band marches over time. Is the rate of change in distance with respect to time constant? What does the rate of change represent?
Time (min)
Distance(ft)
1 2602 5203 7804 1040
Distance marchedRate of change: Change in dependent
Change in independent= Change in distance
Change in time
520-260 2-1
= 260 1
780 - 5203-2
1040 - 7804-3
Rate of change=
Is the rate of change in distance with respect to time constant?
260 ft 1 min
What does the rate of change represent?
The distance the band marches per minute.
= 260 1
= 260 1
Slope: Vertical changeHorizontal change
= riserun
Find the slope of each line
Rise =run
1 Slope = 1 2
Rise =run
Slope = -2 3
-22 3
= change in yChange in x
-5
0
5
-5 0 5
What is the slope of this line?
1. Find your two points on the line. (start at the point furthest to the left)
a. Do you go up or down to get to the next point?
a. If up—the slope is positive
b. If down—the slope is negative
Slope = -
2. Count how far you go up or down and that is the VERTICAL CHANGE
3. Count how far you go right and that is the HORIZONTAL CHANGE
32
Slope Formula: The slope of the line passing through point 1, (x1, y1), and point 2, (x2, y2) is
Examples:1. (1,7) and (6, 4)
2. (-4, -5) and (5, 6)
3. (-3, 2) and (4, -5)
slope = vertical change (rise)horizontal change (run)
change in change in
- x -x2 1
yxy y2 1
4 7
6 1
= - 35
6 -5
5 -4= 11
9
-5 2
4 -3= -7
7= -1
(x1, y1) (x2, y2)
(x1, y1) (x2, y2)
(x1, y1) (x2, y2)
Find the slope of each line
slope = vertical change (rise)horizontal change (run)
change in change in
- x -x2 1
yxy y2 1
(-2,2) (4,2) (x1, y1) (x2, y2)
--
-2 24 -2
= 0 = 0
Slope of a horizontal line = 0
(-4,3)
(-4,-2)
(x1, y1)
(x2, y2) -2 3
-4 -4- =-5
Slope of a vertical line is undefined.
6 0= undefined
4 types of slopePositive Negative
Slope = ZeroSlope = Undefined
Horizontal line Note: the “y-values” are the same
Vertical lineNote: the “x-values” are the same
A babysitter earns $9 for 1 hour and $36 for 4 hours of work. What can you determine about the slope?
It is positive and equals 9.
assignment
pg 298: 23-32,39, 56-58, 60, 62,70-74