10-3 Slope and Rate of Change
Learn to find rates of change and slopes.
10-3 Slope and Rate of Change
Vocabulary
rate of change
slope
10-3 Slope and Rate of Change
The rate of change of a function is a
ratios that compares the difference
between two output values to the
difference between the corresponding
input values.
10-3 Slope and Rate of Change
Additional Example 1A: Using A Table to identify
Rates of Change
Tell whether the rates of change are constant or
variable.
+2
+1
+2 +3
Find the
difference
x 2
4
7
8
10
between
y 5 11 20 23 29
consecutive data
points.
+6
+3
+6 +9
Find each ratio of the
change in y to the
change in x.
The rate of change is constant.
10-3 Slope and Rate of Change
Caution!
Be careful to put the difference in y-values
in the numerator and the differences in
x-values in the denominator when you
write a rate of change.
10-3 Slope and Rate of Change
Additional Example 1B: Using A Table to identify
Rates of Change
Tell whether the rates of change are constant or
+1
+1
+1 +1
variable.
Find the
difference
x 0
1
2
3
4
between
y 0
3
5
8
10
consecutive data
points.
+2
+3
+3 +1
Find each ratio of the
change in y to the
change in x.
The rates of change are variable.
10-3 Slope and Rate of Change
Check It Out: Example 1
Tell whether the rates of change are constant or
variable.
+3
+1
+2 +3
Find the
difference
x 0
2
5
6
9
between
y 5 15 30 35 50
consecutive data
points.
+15
+10 +15 +5
Find each ratio of the
change in y to the
change in x.
The rate of change is constant.
10-3 Slope and Rate of Change
When the rate of
change is constant,
the segments form
a straight line. The
constant rate of
change of a line is
its slope.
10-3 Slope and Rate of Change
Reading Math
Recall that a function whose graph is a
straight line is a linear function.
10-3 Slope and Rate of Change
Additional Example 2: Driving Application
The table shows the driving distances that Jesse
recorded.
A. Determine whether the rates of change are
constant or variable.
The rate of change is constant.
10-3 Slope and Rate of Change
Additional Example 2: Driving Application
B. Graph the data and connect the points with
line segments. If the rate of change is constant,
find and interpret the slope.
The rate of change between
3
any two points is 5 . The
slope of the line is 3 .
5
The slope is
3
. This means he drove 3 mi. every 5 min.
5
10-3 Slope and Rate of Change
Check It Out: Example 2
The table shows the driving distances that Barry
recorded.
Time (min)
1
3
6
9
12
Distance
(miles)
3
6
12
18
24
Determine whether the rates of change are
constant or variable.
3 =3
1
6 =2
3
12 = 2
6
18 = 2
9
The rates of change are variable.
24 = 2
12