FINAL EXAM STUDY GUIDE Answers
Chapter 3: Solving Linear Equations:
1) What is the solution to the following equation?
Answer: x = 9
1
5 - x =11- x
3
2) What is the solution of the equation 19a - 3(a - 6) = a + 63 ? a=3
24
4
3) What is the value of y in the proportion
? z=10
=
5z + 4 z -1
4) What is the solution of the equation
x=30
2
x - 5 = -1?
15
5
5) The formula for converting Fahrenheit to Celsius is C = (F - 32). Use the
9
formula to convert 95˚ F to Celsius.
35 ˚ c
6) In the Poconos, you can ski for $30 per hour plus a $80 fee for equipment
rental. Write equation represents this problem situation
30x + 80 =y
7) The price of chips varies directly as the number of bags bought. If someone
bought 8 bags for $2.32. How much would it cost for 15 bags?
$4.35 Equation : 0.29𝑥 = 𝑦
8)Mary decreased her time in the mile walk from 30 minutes to 24 minutes. What
was the percent of decrease?
20% decrease
9) Tim is choosing between two cell phone plans. Cingular’s plan charges $40 per
month and $100 for activation fee. Verizon’s plan costs $50 per month with an
activation fee of $60.
a) Calculate the total cost for how much each plan would cost including the
activaiton fee after one year .
Cingular: $580
& Verizon $660
b) Write an equation for each phone plan that describes the relationship
between the monthly fee and the activation fee.
40m + 100 = c
& 50m + 60 = c
c) In how many months would both plans cost the same amount of money?
Show your work. Use a complete sentience to explain what your answers
means in the context of the problem. 4 months. After four months both
plans would cost the same. After that Cingular will be cheaper.
Chapter 4: Graphing Linear Equations and Functions
10) Which is a rule for the function?
x
1
y
5
y=3x + 2
3
11
4
14
5
17
11) What is the equation for the given input output table?
Input
(x)
Output
(y)
0
1
2
3
4
-3
2
7
12
17
y=5x – 3
12) The domain of the function y = -4x - 5 is { -3, 0, 3, 6}. State the range.
{-29, -17, -5, 7}
13. Amy is performing a biology experiment. The table below shows a relationship
between the temperature (t) and number of bacteria in an experiment (n)
Write the equation that shows the relationship of the number of bacteria in the
experiment as a function of the temperature.
t
N
2
9
4
15
6
21
8
27
10
33
n=3t+3
14)You can order custom posters for $2.32 per poster plus a service fee of $20.
Write an equation to describe the total cost (c) to enlarge (p) posters?
c= 2.32p + 20
15) Graph x = 3
( vertical line through 3)
16) Graph y = -2
(horizontal line though -2)
17) Evaluate the function f (x) = 8x - 2 when x = -4 .
f(x)= -34
1
18) Given the function f (x) = x - 3, find x when f (x) =1 .
5
x=20
1) A line is graphed on the coordinate plane below. What is the slope of the line?
Slope: 2/3
20) The table shows the cost of a yoga class for a given amount of time.
What is the cost per minute?
Time(minutes)
Cost(Dollars)
20
$6.60
25
$8.25
30
$9.90
Cost per minute $0.33
21)Find the x- and y- intercept for the equation 5x – 6y = 30. Write your answers
as an ordered pair.
y= -5 (0, -5) x=6 (6, 0)
22)What phrase would be the units for the rate of change for the graph shown?
Temperature per second.
23)In the accompanying graph, if point S has coordinates (-a, b), which point has
coordinate (-b, -a)?
Point A
24) A revenue of $1900 is obtained from the sales of item A at $30 each and item B at $40
each.
a) Write an equation in standard form that shows the relationship between the numbers of
each item sold and the revenue.
30x + 40y = 1900
b) Graph the equation using any method.
C) If you sold 10 of Item A, how many item B’s would you need to sell to get $1900 in
revenue.
40 of item B need to be sold.
Chapter 5: Writing Linear Equations
25)Which equation of a line is parallel to the line y = ⅓x + 2 and passes
through the point ( 12, -2 )?
y=1/3x – 6
26)Over time a teacher had gathered data to predict the number of points (y)
that student will grow that will occur over (x) lessons. After making a scatter
plot of the data, he determines the equation of a line of best fit. The equation
is shown below.
𝑦 = .2𝑥 + 4
Based on the equation, how many points will the students grow over 20
years?
8 points
27) The graph of a line with slope of -4 passes through the point (3, -1). Write a
linear equation for that line.
y=-4x+11
28) Find the slope of a line that has the equation 6x - 2y =10 .
Slope= 3
29)_ This scatter plot shows a relationship between the number of hours of
exercise per week and the resting heart rate.
Write an equation for the line of best fit.
−25
𝑦 = 6 𝑥 + 80
30) The graph of a line passes through the points (1,3) and has a slope of 2. Write an
equation in point-slope form.
𝑦 − 3 = 2(𝑥 − 1)
31) Write an equation in standard form that represents the graph below?
x – y = -2
Mixed Practice: Choose the best answers.
32) Which number is between -10 and -15?
[A]
- 82
[B]
- 188
[C]
- 325
[D] - 441
33) Which equation of line is perpendicular to 4x + y = 7 and passes through the
point
( -4, 1 )?
[A] y = 4x + 2
[B] y = -4x + 2
1
1
[C] y = x + 8
[D] y = x + 2
4
4
34)Which of the following points is NOT a solution to the linear function y = 7x - 2
?
[A] (0, -2)
[B] (2, 12)
[C] (1, 5)
[D] (1, 9)
35) Which table is represented by the graph?
[A]
[B]
[C]
[D]
36) Which of the following relations represents a function?
[A]
{(5, 1), (2, 3), (6, 7), (5, 7)}
[B]
{(2, 8), (7, 6), (4, 9), (4, 3)}
[C]
{(0, -1), (6, -2), (7, -3), (8, -2)}
[D]
{(0, -2), (7, 5), (6, 5), (0, 1)}
37) Which of the following tables demonstrates a direct variation equation?
[A]
x
y
0
5
1
7
2
9
3
11
x
y
x
y
0
0
0
1
1
7
1
3
2
14
2
5
3
21
3
8
x
0
1
y
0
6
38) Arrange the following numbers from least to greatest.
2
10
3
12
[B]
[C]
2𝜋, √10,
√10,
3. 2̅,
2√5,
2
37 ,
2
3. 2̅,
37
2√5,
2𝜋
39) Which equation describes the line passing through the points (5, 12) and (2,
4.8)?
[A] y = 2.4x
[B] y = -2x
[C] y = -3.4x
[D] y = 2.2x
40) Find the value that would be contained in the range of the function shown below?
[A] -1
[B] 3
[C] 2
[D] 4