1.1
Graphs & Graphing Utilities
Monday, October 20
Math for College Readiness
Rectangular Coordinate System
Coordinate Grid: a grid formed
by two perpendicular number
lines called axes.
(2, 3): The number 3
x-axis: the horizontal axis on
the coordinate plane
y-axis: the vertical axis on the
coordinate plane
(2, 3)
x-coordinate: The first number
in an ordered pair, which tells
the distance to move right or
left from (0, 0)
Ordered Pair: a pair of
numbers used to locate a point
on a coordinate grid
y-coordinate: The second
number in an ordered pair,
which tells the distance to
move up or down from (0, 0)
(2, 3): The number 2
Plot the following
points:
1. (0, 10)
2. (-2, 3)
3. (-10, 3)
4. (-4, -2)
5. (-7, -10)
6. (0, -5)
7. (7, -10)
8. (4, -2)
9. (10, 3)
10. (2, 3)
Graphing an Equation:
Point-Plotting Method
𝑥
-3
-2
-1
0
1
2
3
𝑦 = 4 − 𝑥2
(𝑥, 𝑦)
Graphing an Equation:
Point-Plotting Method
𝑥
-3
-2
-1
0
1
2
3
𝑦 = 𝑥 −3
(𝑥, 𝑦)
1.1
Graphs & Graphing Utilities
Tuesday, October 21
Math for College Readiness
Identify the 𝑥- and 𝑦- intercepts.
Identify the 𝑥- and 𝑦- intercepts.
Identify the 𝑥- and 𝑦- intercepts.
Identifying Intercepts
No 𝑥- intercept
1 𝑦- intercept
Identifying Intercepts
No 𝑥- intercept
No 𝑦- intercept
Identifying Intercepts
3 𝑥- intercepts
1 𝑦- intercept
Identifying Intercepts
1 𝑥- intercept
No 𝑦- intercept
Interpreting Data from Graphs
Please open your textbook to page 96.
Interpreting Data from Graphs
Here are two mathematical models that
approximate the data displayed by the line graphs:
Wife is under 18 at time of marriage:
𝑑 = 4𝑛 + 5
Wife is over 25 at time of marriage:
𝑑 = 2.3𝑛 + 1.4
Where 𝑛 is the number of years after marriage and
𝑑 is the percentage of marriages ending in divorce.
Interpreting Data from Graphs
a) Use the appropriate formula to determine the
percentage of marriages ending in divorce after 10 years
when the wife is over 25 at the time of the marriage.
Recall: 𝑑 = 2.3𝑛 + 1.5
Observe: 𝑛 = 10
We have: 𝑑 = 2.3 10 + 1.5
= 23 + 1.5
= 24.5
Finally, the model indicates that 24.5% of marriages end
in divorce after 10 years of marriage when the wife is
over the age of 25 at the time of the marriage.
Interpreting Data from Graphs
b) Use the appropriate line graph in Figure 1.11 to determine the
percentage of marriages ending in divorce after 10 years when
the wife is over 25 at the time of the marriage.
Observe: The line graph on page 96 of the textbook.
Locate 10 on the horizontal axis and locate the point
above 10.
Read across to the corresponding percent on the
vertical axis.
Finally, the graph indicates that 25% of marriages end in divorce
after 10 years of marriage when the wife is over the age of 25 at
the time of the marriage.
Interpreting Data from Graphs
c) Does the value given by the mathematical model
underestimate or overestimate the actual percentage of
marriages ending in divorce after 10 years when the wife is over
the age of 25 as shown by the graph? By how much?
Recall from Part a): model indicated 24.5%
Recall from Part b): graph indicated 25%
So, 24.5% is slightly less than 25%. The difference between these
percentages is 25% − 24.5% = 0.5%. This means that the
mathematical model underestimated the actual percentage by
0.5%, providing a fairly accurate description of the data.
Review
Wednesday, October 22
Math for College Readiness
I Do, You Do, We Check
Work in a group of 3 to complete the activity on Section 1.1.
The Procedure:
Both partners will work on the problem.
Once both partners believe they have the final answer, check to see if
your answers are the same.
If the answers match, you may move on to the next problem.
If the answers do not match, look over each other’s work and try
to find the error.
Once you have completed two problems, raise your hand and I will
come check them.
If all 2 problems are correct, you may move onto the next set of
problems.
If any of your problems are incorrect, you must try them again
and I will come check when you think you have corrected your
mistake.
I Do, You Do, We Check Review
Quiz: 1.1
Thursday, October 23
Math for College Readiness