Download LT 8.4 Practice Problems

Mathematical Investigations II
Name
Mathematical Investigations II
Linear Thinking
Review – Part I
1.
Write an equation of the line with slope 5 that goes through (1,3).
2.
Write an equation of the line through the points (1,6) and (2,-3).
3.
Write an equation of the line parallel to 3x - 4y = 6, which passes through (-2,4).
4.
Write an equation of the line with an x-intercept of 3 and perpendicular to
4x = 2y - 6.
5.
Write a recursive and an explicit formula for the following arithmetic sequences:
a.
2, 8, 14, 20, 26, ….
b.
1, -2, -5, -8, -11, ….
c.
The arithmetic sequence with a2 = 4 and a8 = -14.
Linear Thinking 8.1
Rev. S03
Mathematical Investigations II
Name
6.
Graph the line y = 2x + 3 on the
xy-coordinate plane.
7.
a. Graph the line -2x - 3y = 6 on the
xy-coordinate plane.
b. Shade in the region where -2x - 3y < 6.
8.
Which of the following relationships are linear? Explain your reasoning
a. Population of the United States vs. year.
Year
Population
(in millions)
1790
1860
1910
1960
2000
4
31
92
179
281
b. Area of a circle vs. its diameter.
c. Distance traveled vs. time for a car traveling a constant speed of 60 mph.
d. Volume of a box with height 10 inches vs. the area of its base.
Linear Thinking 8.2
Rev. S03
Mathematical Investigations II
Name
9.
The following table shows the Public debt in trillions of dollars for some of the years
from 1991 to 2001.
Year
National Debt
1991
3.67
1992
4.06
1993
4.41
1994
4.69
1996
5.22
1997
5.41
1998
5.53
1999
5.66
2000
5.67
2001
5.81
a. If you were to graph the data, what would x and y represent?
x=
y=
b. What would be an appropriate window for this data?
<x<
<y<
c. Use your calculator to make a scatter plot of the data and derive the median-median
line and the linear regression line.
d. Is there a linear relationship between the year and the Public debt?
Explain your reasoning.
e. What does the slope of each of these lines mean?
f. What does the y-intercept of each of these lines mean?
g. Using your equation in part c), estimate the Public debt for the year 1995.
h. Estimate the Public debt for the year 2003.
i. How accurate do you believe that your answers for g) and h) are? Explain.
Linear Thinking 8.3
Rev. S03
Mathematical Investigations II
Name
10.
The following numbers are salinity values for water specimens taken from North
Carolina’s Pamlico Sound.
7.7
13.1
14.1
4.3
12.2
16.4
5.9
8.2
7.1
5.0
12.6
8.9
10.4
8.3
8.5
7.7
13.2
13.2
9.5
13.6
14.2
a.
Find the five point summary for this data.
b.
Draw a box plot and a stem plot for this data.
c.
Find the mode and the mean.
Linear Thinking 8.4
12.0
10.4
15.1
12.6
10.4
9.0
12.2
8.3
9.3
Rev. S03