"Functions and Linear Modeling Worksheet With Answer Key"

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Algebra
Name __________________________________
CHAPTER 4 REVIEW
FUNCTIONS AND LINEAR MODELING
Period ______ Date ______________________
EXCEPT YOUR GRAPHS, DO ALL YOUR WORK ON A SEPARATE PIECE OF PAPER.
BE SURE TO NUMBER ALL QUESTIONS AND SHOW ALL YOUR WORK.
4
1.
Write in point-slope form the equation of the line that passes through the point (2, -6) with slope −
.
5
2.
Write in point-slope form an equation for the line shown to the right.
2
3.
Rewrite the equation �� + 4 = −
(�� − 7) in slope intercept form.
5









4.
Rewrite the equation 4�� + 3�� = −39 in slope-intercept form. What is
the slope of the line?


5.
Write in point-slope form the equation of the line passing through the

points (−2,5) and (10, −7).

6.
For her Algebra final exam, Patty Patriot will have to take a test worth 100 points. The test only has two types

of questions: multiple choice questions, each of them worth 2 points, and free response questions, each of
them worth 4 points. Patty’s teacher announced that he has not decided yet how many questions of each type
the final exam will have. Write an equation relating the number of multiple choice questions and the number
of free response questions the final exam could have. Make sure to define your variables.
3
7.
Rewrite the equation �� =
�� + 4 in standard form.
7
In 8-11, solve each equation. Be sure to clearly show all steps to receive full credit. You may leave your answers
as simplified fractions: no decimals.
8.
9.
10
x
5
5
6
2
x
1
7
x
15
3
x
4
2
x
5
 x
10
5
2
7
x
5
10.
11.
15
2
3
x
1
2
Identify the slope and y-intercept of each line and use that information to graph the line.
5
5
12.
13.
14.
�� =
�� − 3
�� = 4�� + 1
�� = −
�� − 2
8
3
m =
; b =
.
m =
; b =
.
m =
; b =
.
SEE OTHER SIDE
Algebra
Name __________________________________
CHAPTER 4 REVIEW
FUNCTIONS AND LINEAR MODELING
Period ______ Date ______________________
EXCEPT YOUR GRAPHS, DO ALL YOUR WORK ON A SEPARATE PIECE OF PAPER.
BE SURE TO NUMBER ALL QUESTIONS AND SHOW ALL YOUR WORK.
4
1.
Write in point-slope form the equation of the line that passes through the point (2, -6) with slope −
.
5
2.
Write in point-slope form an equation for the line shown to the right.
2
3.
Rewrite the equation �� + 4 = −
(�� − 7) in slope intercept form.
5









4.
Rewrite the equation 4�� + 3�� = −39 in slope-intercept form. What is
the slope of the line?


5.
Write in point-slope form the equation of the line passing through the

points (−2,5) and (10, −7).

6.
For her Algebra final exam, Patty Patriot will have to take a test worth 100 points. The test only has two types

of questions: multiple choice questions, each of them worth 2 points, and free response questions, each of
them worth 4 points. Patty’s teacher announced that he has not decided yet how many questions of each type
the final exam will have. Write an equation relating the number of multiple choice questions and the number
of free response questions the final exam could have. Make sure to define your variables.
3
7.
Rewrite the equation �� =
�� + 4 in standard form.
7
In 8-11, solve each equation. Be sure to clearly show all steps to receive full credit. You may leave your answers
as simplified fractions: no decimals.
8.
9.
10
x
5
5
6
2
x
1
7
x
15
3
x
4
2
x
5
 x
10
5
2
7
x
5
10.
11.
15
2
3
x
1
2
Identify the slope and y-intercept of each line and use that information to graph the line.
5
5
12.
13.
14.
�� =
�� − 3
�� = 4�� + 1
�� = −
�� − 2
8
3
m =
; b =
.
m =
; b =
.
m =
; b =
.
SEE OTHER SIDE
Graph each line and give the coordinates of a pair of points on the line.
15.
16.
�� = 3
�� = −6
x
y
x
y
Identify the x- and y-intercept of each line and use that information to graph the line.
17.
18.
3�� + 5�� = 30
2�� − 6�� = 24
x-int =
;
x-int =
;
y-int =
.
y-int =
.
Identify the slope and a point of each line and use that information to graph the line.
1
5
19.
20.
�� = 1 +
(�� + 3)
�� + 4 = −
(�� − 5)
4
6
m =
;
m =
;
point = ( , )
point = ( , )
In questions 21 and 22, use unit analysis and unit rates to rewrite each problem
1 hour = 60 minutes
1 kilometer = 1000 meters
in the units indicated. Show all your work.
1 liter = 100 centiliters
1 minute = 60 seconds
21.
Express 16 pints to liters.
1 liter = 10 deciliters
1 liter = 1000 milliliters
1 mile = 1.6 kilometers
22.
Express 8 minutes per mile to seconds per kilometer.
1 foot = 12 inches
1 gallon = 4 quarts
1 inch = 2.54 centimeters
1 mile = 5280 feet
1 gallon = 3.8 liters
1 quart = 2 pints
Algebra
Answers
CHAPTER 4 REVIEW
FUNCTIONS AND LINEAR MODELING
4
1.
Write in point-slope form the equation of the line that passes through the point (2, -6) with slope −
.
5
4
�� + 6 = −
(�� − 2)
5
2.
Write in point-slope form an equation for the line shown to the right.
3
3
3
( �� − 3 ) or �� − 2 =
�� + 1 =
(�� − 7) or �� + 4 =
(�� + 1)
4
4
4
2








3.
Rewrite the equation �� + 4 = −
(�� − 7) in slope intercept form.

5
2
6
�� = −
�� −

5
5

4.
Rewrite the equation 4�� + 3�� = −39 in slope-intercept form. What is

the slope of the line?

4
4
�� = −
�� − 13; �� = −

3
3
5.
Write in point-slope form the equation of the line passing through the points (−2,5) and (10, −7).
or
�� − 5 = −(�� + 2)
�� + 7 = −(�� − 10)
6.
For her Algebra final exam, Patty Patriot will have to take a test worth 100 points. The test only has two types
of questions: multiple choice questions, each of them worth 2 points, and free response questions, each of
them worth 4 points. Patty’s teacher announced that he has not decided yet how many questions of each type
the final exam will have. Write an equation relating the number of multiple choice questions and the number
of free response questions the final exam could have. Make sure to define your variables.
2�� + 4�� = 100;
where x = the number of multiple choice questions in the final and
y = the number of free response questions in the final
3
7.
Rewrite the equation �� =
�� + 4 in standard form.
7
or 3�� − 7�� = −28
−3�� + 7�� = 28
In 8-11, solve each equation. Be sure to clearly show all steps to receive full credit. You may leave your answers
as simplified fractions: no decimals.
9.
8.
10
x
5
5
6
2
x
1
7
x
15
3
x
4
2
x
5
1
�� = 8
�� = −
3
 x
10
5
2
7
x
5
10.
11.
15
3
x
1
2
2
�� = −4
�� = −9
Identify the slope and y-intercept of each line and use that information to graph the line.
5
5
12.
14.
13.
�� =
�� − 3
�� = −
�� − 2
�� = 4�� + 1
8
3
m = 4; b = 1.
5
5
m =
; b = −3.
m = −
; b = −2.
8
3
Graph each line and give the coordinates of a pair of points on the line.
15.
16.
�� = 3
�� = −6
x
y
x
y
3
1
0
‒6
3
‒2
3
‒6
3
0
‒1
‒6
Identify the x- and y-intercept of each line and use that information to graph the line.
17.
18.
3�� + 5�� = 30
2�� − 6�� = 24
x-int =
(10,
0);
x-int =
(12,
0);
y-int =
(0, 6).
y-int =
(0,
‒4).
Identify the slope and a point of each line and use that information to graph the line.
1
5
19.
20.
�� = 1 +
(�� + 3)
�� + 4 = −
(�� − 5)
4
6
5
1
m =
;
m =
;
6
4
point =
point =
(5, −4)
(−3, 1)
In questions 21 and 22, use unit analysis and unit rates to rewrite each problem
1 hour = 60 minutes
1 kilometer = 1000 meters
in the units indicated. Show all your work.
1 liter = 100 centiliters
1 minute = 60 seconds
21.
Express 16 pints to liters.
1 liter = 10 deciliters
1 ����������
1 ������������
3.8 ������������
1 liter = 1000 milliliters
16 ���������� ×
×
×
= 7.6 ������������
1 mile = 1.6 kilometers
2 ����������
4 ������������
1 ������������
1 foot = 12 inches
22.
Express 8 minutes per mile to seconds per kilometer.
1 gallon = 4 quarts
1 inch = 2.54 centimeters
8 ��������������
60 ��������������
1 ��������
1 mile = 5280 feet
×
×
= 300 �������������� ������ ������������������
1 gallon = 3.8 liters
1 ��������
1 ������������
1.6 ��������������������
1 quart = 2 pints