Name: ______________________
Class: _________________
Date: _________
Unit 5 Study Guide 2016
Short Answer
1. a. Which of the following tables represent linear relationships?
Time
0
1
2
3
4
Table 1
(s) Distance (m)
5
10
12
16
20
Table 2
Distance (km) Money ($)
0
0
1
10
2
20
3
30
4
40
Table 3
Days
Money ($)
0
10
1
8
2
6
3
2
4
4
b. Write an equation for one of the tables that represents a linear relationship.
c. Which table(s), if any, represents a proportional relationship? Explain.
2. Each graph below represents a linear relationship between time and distance.
For each graph, describe what is the rate of change?
1
ID: A
Name: ______________________
ID: A
3. Mark opens a bank account with $20. Each week he plans to put in $5.
a. Make a table to show the total amount of money Mark has in his bank account. Show the
amount he has in his account from 0 to 10 weeks.
b. Make a graph that matches the table.
c. Write an equation to represent the total money Mark has in his account over time.
d. In which week will Mark have a total of $60. Explain your reasoning.
4. Solve each equation to find the value of x.
a. 4x + 10 = 22
b. 3x + 9 = 6x
c. 2(x + 3) = 18
d. 2x + 15 = 27 – 4x
2
Name: ______________________
ID: A
5. To encourage customers, a new movie theater is offering different ways to pay for a movie.
• Members: $75 a year plus $2 per movie.
• Nonmembers: $5.75 to see a movie.
a. Make one table that shows the number of movies n and the cost for members C1 . Make another
table that shows the number of movies n and the cost for nonmembers C2 . For both tables,
include values of n from 0 to 50 movies, in increments of 10.
Number
Cost
Number
Cost
b. On the same set of axes, graph the relationship of cost and number of movies for members and
for nonmembers.
c. Write equations that you can use to calculate the cost for members C1 and non-members C2 , for
any number of movies n.
Equation for members: _________________________
Equation for nonmembers: ______________________
6. Big A's Bike Rentals charges $300 plus $20 per bike to rent bikes for a week. Little Cheeper's rental shop
charges $50 plus $35 per bike for a week. Which company is the better deal?
3
Name: ______________________
ID: A
7. Given one of the representations below, find the other two.
Table
Graph
Equation
y=
a. Find the y-intercept for each representation above.
4
1
x+1
3
Name: ______________________
ID: A
8. Use the graph below to answer (a)-(d).
a. List the coordinates of three points on the line.
b. Which equation below is the equation of the line?
i.
y=x+4
i i. y = 0.5x + 2
i i i. y = 0.5x - 5
c. Does the point (56, 35) lie on the line?
d. Does the point (–20, –8) lie on the line?
5
iv. y = 4 - 0.5x
Name: ______________________
ID: A
9. Here is a graph of three lines.
a. Complete the chart.
line
A
B
C
constant rate of change
y-intercept
x-intercept
b. Here are the equations of the three lines. Match each line with its equation.
y = 2 + x,
y = −4 + 2x,
y = 3−x
line A: ____________,
line B: ____________,
10. Here is a graph of a line:
a. Complete this table.
x
–3
0
2
5
7
10
100
y
6
line C: ____________
Name: ______________________
ID: A
11. Marsha said there are two ways to solve the equation 3x + 15 = 24
3x + 15 = 24
3x = 9
x=3
subtract 15 from each side
divide each side by 3
3x + 15 = 24 divide each side by 3
x+5 = 8
subtract 5 from each side
x=3
a. Are both strategies correct? Explain.
b. Which strategy do you think is easier? Explain.
12. Find x if
a. x + 7 = 20
b. 3x + 7 = 20
c. −2x + 7 = 20
d. How are the solutions similar? How are they different?
13. Solve the following equations for the value of x:
a. 3x + 5 = 4x – 10
b. 4x + 10 = 6x – 8
d. 3x – 11 = 8x – 21
e . 3x + 24 = 12
c. 3x + 10 = 5x
14. Find the slope and y-intercept of the line represented by each equation.
a. y = 2x – 10
b. y = 4x + 3
d. y = 2.6x
e . y = 7x + 1
c. y = 4x – 4.5
7