Name: _____________________________________________ Period: ______ Test Grade: ______/100
Unit 5 Study Guide (Ans. Key)
Knowledge and Understanding
1. How is unit rate related to the slope of a function line? Justify your answer. (8 points)
Possible answer: Slope is the rate of change, or unit rate, that shows how the dependent
value changes when the independent value increases by 1. It shows the change of y over x
2. When two linear functions share the same rate of change, what might be different about their tables,
graphs and equations? (8 points)
Possible answer: The y-intercept might be different. This would be seen in the equation (the b
would be different in y  mx  b , the graphs would be different (the lines would cross the yaxis at different locations), the tables would have different y-values. The lines would be
parallel since they have the same rate of change.
Proficiency of Skills
3. Determine the slope of the line that passes through the points (0, -4) and (0, 5). (5 points)
Undefined m 
5  (4) 9

when the 0 is in the denominator the slope is undefined.
00
0
4. Determine the equation of the line graphed below. (5 points)
y  2x  3
5. Graph the line containing the points (-5, 1) and (0, 6) on the coordinate plane below. Then use the graph to
determine the equation of the line. (8 points)
y  x  7
6. Determine the equation of the line in slope-intercept form given the table. (8 points)
x
-1
0
1
y
-2
2
6
y  4x  2
7. Determine the equation of the line that intersects the x-axis at (7, 0) and the y-axis at (0, 7). (8 points)
y  x  7
Application
8. A clothes designer manufactures 112 pairs of jeans every 8 minutes. What is the unit rate (slope) of the
line and what does it represent (what does it mean)? (5 points)
The slope is 14; it represents the number of jeans manufactured every minute
9. Kell works at an after-school program at an elementary school. The table below shows how much money
he earned every day last week. (8 points)
Mariko has a job mowing lawns that pays
Wednesday
Friday
Monday
$7 per hour. Determine who would make
Time worked
1.5 hrs
2.5 hrs
4 hrs
more money for working 10 hours (Kell
Money
$21.00
$33.60
or Mariko) by showing how much each
$12.60
earned
guy would make for working 10 hours.
8.4/1
8.4/1
Slope
8.4/1
Slope= amount of earned divided by the hours worked
Kell would earn $84 for 10 hours of work and Mariko would earn $70 for 10 hours of
work.
10. The cost to rent a bouncy castle at Mario’s Amusements can be found using the equation c  35h where c
is the cost in dollars and h is the number of rental hours.
Luigi’s Party World uses the following table to determine the total cost for renting a bouncy castle.
Hours of
Rental
2
4
6
8
10
Cost of Rental
($)
65
130
195
260
325
Which company’s rental rate is the better
buy? Justify your answer. (8 points)
**Use the table to find the change of y over
the change of x**
Luigi’s is a better buy because they only charge $32.50 per hour and Mario charges $35 per
hour
11. The state fair will admit one person for $6, two people for $9, three people for $12, etc…
Write an equation that models the price of admittance as a function of the number of people entering.
(8 points)
X (# of people)
1
2
3
Y (Cost)
6
9
12
y  3x  3 where y is the cost in dollars for x people
12. The distance traveled on a trip is directly proportional to the speed of the car. A car traveled 300 miles in
six hours. Write an equation to represent y, the distance the car would travel in x hours. (5 points)
y  50 x
Distance
(meters)
13. The graphs below show the distance two cars have traveled along the freeway over a period of several
seconds. (2 points)
Car A is traveling 30 meters per second.
Which equation from
y
those shown to the
A. y = 85x
right is the best choice
A
B. y = 60x
for describing the
distance traveled by car
C. y = 30x
B after x seconds?
B
D. y = 15x
Time
(sec)
x
14. Explain how the similar triangles below are related to each other and to the slope of the line. (8 points)
The two triangles are similar-they are proportional. They have the same shape but not the
same size. The slope of the hypotenuse of each triangle is 2/3 when you simplify the larger
triangle’s hypotenuse using the Pythagorean Theorem.
15. Which is the equation of a line that intersects the y-axis at -3 and has a slope of -2? (2 points)
A. y = -3x – 2
B. y = -2x – 3
C. y = -3 + 2x
D. y = -2x + 3
16. Which of the following is an example of a nonlinear function? (2 points)
A. y = 5x – 4
B. 2x – 6y = 8
C. y = -4
D. y = x2 + 9
17. Which of the functions on the graph below has the greatest rate of change? (2 points)
A. Function A
B. Function B
Function A because it has the steepest slope.
C. Function C
D. Function D