Lesson 7.2.4
HW: 7-71 to 7-76
Learning Target: Scholars will connect negative slopes with decreasing rates of change and a slope of
zero with no change. Scholars will also use slope to describe the average rate when the rate is not
constant.
In recent lessons, you have learned how to find the slope of a line. You have also learned how slope
describes the rate of change and the steepness of a line on a graph. In this lesson, you will learn about
other information that the slope of a line can tell you.
7-67. Which is steeper: a line with a slope of
know? Explain.
or a line with a slope of
? How do you
7-68. Compare the two lines in the graph at right.
How are the two lines the same? How are they different?
1. Each line on this graph describes how much money a person has in his or her wallet over
time (in days). Explain what is happening to the amount of money each person has. Be
specific.
2. To describe how person A’s amount of money is changing, the unit rate (slope)
represents the amount that is added each day. Since the value of money is increasing, the
slope is positive. But what should you do when the value is decreasing? How should the
decrease be reflected in the rate (slope)? Discuss this with your team.
3. Remember that the slope ratio compares how the change on the y-axis compares to the
change on the x-axis. Lines that go up from left to right show positive rates of change, or
positive slopes, while lines that go down from left to right show negative rates of change,
or negative slopes.
Find the slope of each line in the graph.
7-69. WHAT IF IT DOES NOT GROW?
The graph at right shows three different lines.
4. Describe each line in words. Is it increasing or decreasing? Quickly or slowly?
5. Line B is different from the other two lines. As the x-value increases, what happens
to y?
6. Slope is a comparison of
. Pick two points on line B. How can you use a
number to represent the change in y between these two points? Use this number or the
change in y to write a slope ratio for line B.
7. Recall that the units for the “change in y” are the same as the y-axis, and that the units
for the “change in x” are the same as for the x-axis. What are the rates of growth for
lines A and C? Be sure to include units.
8. Express the rates in part (d) as unit rates.
7-70. PERSONAL TRAINER
To prepare for biking long distances, Antoine has been trying to keep a steady pace as he
bikes. However, since his hometown has many hills, he ends up biking faster and slower during different
parts of his ride.
To track the distance and time when he trains for the triathlon, Antoine purchased a special watch that
tells him how far he has traveled at specific time intervals. With the push of a button, he can set it to
record data. Then, at the end of his workout, the watch gives him a list of the data.
9.
On his first bike ride around town, he recorded
several times and distances. These measurements are shown in the table at
right. According to the table, does he appear to be traveling at a constant rate? Explain
your reasoning.
10. Draw and label a graph that extends to 40 minutes on the x-axis and to at least 15 miles
on the y-axis. Plot Antoine’s time and distance data on the graph. What type of graph is
this?
11. Draw a trend line that best represents Antoine’s data. Then extend it to predict about
how long it will take him to bike 10 miles (his normal long distance workout).
12. What is Antoine’s general rate during his bike ride? Find the slope (rate of change) of
the trend line you drew in part (c) to determine his general rate.
7-71. For each pair of slope ratios, decide if they are equivalent (=), or if one slope is greater. If the
slopes are not equal, use the greater than (>) or less than (<) symbol to show which is greater.
1.
,
2.
,
3.
,
7-72. Describe the associations in the two graphs below. Remember to describe the form, direction, and
outliers.
7-73. Ella and her study team are arguing about the slope of the line in the
graph at right. They have come up with four different answers:
correct? Justify your answer.
7-74. Solve each of the following equations.
4.
x+ = x−
5. 0.15(w + 2) = 0.3 + 0.2w
6.
7. 3(2x − 7) = 5x + 17 + x
,−
,−
and
. Which slope is
7-75. Salami and More Deli sells a 6-foot sandwich for parties. It weighs 8 pounds. Assume the weight
per foot is constant. 7-75 HW eTool (Desmos).
8. How much does a sandwich 0 feet long weigh?
9. Draw a graph showing the weight of the sandwich (vertical axis) compared to the length
of the sandwich (horizontal axis). Label the axes with appropriate units.
10. Use your graph to estimate the weight of a 1-foot sandwich.
11. Write a proportion to find the length of a 12-pound sandwich.
7-76. Find the area of the entire rectangle in each diagram below. Show all work.
a.
b.
c.
d.
Lesson 7.2.4


7-67.
than
7-68.
1.
2.
is steeper. Possible reasons:
represents a greater unit rate, or
is greater
.
See below:
Both start at the same y-value, but one increases and one decreases.
Person A starts with $12 and adds $2 to her account every day. Person B starts
with $12 but takes $2 out of her account every day.
3. It should be negative, to reflect the amount of decrease in the value for each
week.

4. slope A =
= 2, slope B =
= −2
7-69. See below:
1. Line A is increasing quickly, line B does not increase or decrease, line C
is decreasing slowly.
2. The y-value does not change.
3. Change can be represented with 0. The slope ratio could be
4. A:

.
C:
5. A:
C:
7-70. See below:
1. No, he is not. For example, the rate between the start and the 3rd minute is 10
miles per hour and the rate between the 5th and 8th minute is 20 miles per hour.
2. The data forms a scatterplot, shown below.
3. Answers vary, but a line through (0, 0) and (16, 4.5) is reasonable; About 36
minutes.
4. Answers vary, but answers should be approximately 15 miles per hour.

7-71.
1.
2.
3.

7-72. Graph 1: positive, non-linear association, with one outlier, Graph 2: positive linear
association with no outliers.

7-73. The slope of
is correct because the line is decreasing and for every four units
that the line moves to the right, it also goes down 3 units.

7-74.
1.
2.
3.
4.

7-75. See below:
1. 0 pounds
2. The graph should show a line with positive slope. Units labeled on the axes
should be in pounds (vertical axis) and feet (horizontal axis).

3.
4.
7-76.
1.
2.
3.
4.
See below:
>
=
<
See below:
x = 12
w=0
x=1
No solution
pounds
9 feet
See below:
4896 sq. units
91 + 13x sq. units
900 sq. units
336 sq. units