3.1
3.1 Slope
Slope
All of the patterns of change you have explored in this unit
involved constant rates of change. This means all of these
relationships have been __________.
For example, you worked with walking rates expressed as
meters per second and pledge rates expressed as dollars per
mile. In these situations you found that the rate affects the
following things:
· in a graph . . . the steepness
· in a table . . . the amount of increase/decrease in the y values
· in an equation . . . the coefficient of the independent variable
The method for finding the steepness of stairs suggests a way
to find the steepness of a line. A line drawn from the bottom
step of a set of stairs to the top step touches each step in one
point.The rise and the run of a step are the vertical and the
horizontal changes, respectively, between two points on the
line.
The steepness of the line is the ratio of rise to run, or vertical change
to horizontal change, for this step.We call this ratio the slope of the line.
slope
slope
graph . . . steepness
rise
run
table. . . amount of increase/descrease
change in y
change in x
equation . . . aka. constant rate of change
coefficient of the independent variable: CR or m
There are 4 types of slope:
Positive
Negative
Zero
Undefined
Using a graph...
How do you find slope?
Identify 2 points on the line
1. ________________________________________
Find the RISE and RUN between the
2. ________________________________________
Make the fraction rise/run
3. ________________________________________
reduce if possible
4. ________________________________________
points
1. Identify points
2. Find the rise and run
3. Write the fraction
4. Reduce
1.
2.
3.
4.
A.
B.
C.
Using a table...
How do you find slope?
Find the change in y values
1. ________________________________________
Find the change in x values
2. ________________________________________
Make the fraction change in y/change
3. ________________________________________
reduce if possible
4. ________________________________________
in x
1.
2.
3.
4.
A.
x
0
1
2
3
y
7
11
15
19
Find the change in y
Find the change in x
Write the fraction
Reduce
B.
1.
2.
3.
4.
C.
1.
2.
3.
4.
Find the change in y
Find the change in x
Write the fraction
Reduce
Find the change in y
Find the change in x
Write the fraction
Reduce
x
3
5
7
9
y
12
14
16
18
D.
x
y
0
4
2
-2
7
-17
10
-26
1.
2.
3.
4.
Find the change in y
Find the change in x
Write the fraction
Reduce
E.
1.
2.
3.
4.
x
y
0
6
5
8
10
10
15
17
Find the change in y
Find the change in x
Write the fraction
Reduce
x
3
5
9
15
y
12
9
3
-6
OAA Examples: