DMA 50 Worksheet #1
Introduction to Graphs: Analyzing, Interpreting, and Creating Graphs
A graph will be given followed by a set of questions to answer. Show your work.
The bar graph below shows the number of students by major in the College of Arts and Sciences. Answer the
question.
1) How many students are majoring in Math?
2) About how many students are in the College of Arts and Sciences?
3) Which major has the largest number of students?
4) Which major has about 150 students?
5) How many more students are majoring in math than in science?
6) What is the average number of students taking History, English, and Science? Round your answer to the
nearest whole student if necessary.
7) The English department assigns a counselor to each student majoring in English. Each counselor is assigned
50 students. How many counselors are needed?
8) The science department is planning to buy some new equipment. They want to make sure that there is one of
the new machines for every 5 students majoring in science. If each machine costs $850, how much should
they budget for the new equipment?
1
Use the pictograph to answer the questions.
9) This pictograph shows projected sales of compact disks (CDs) for a popular rock band for seven consecutive
years. Between which two consecutive years is the greatest decline in sales indicated?
Year Projected CD Sales
2015 ⊙⊙
2014 ⊙⊙⊙⊙⊙⊙
2013 ⊙⊙⊙⊙⊙⊙⊙⊙⊙
2012 ⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙
2011 ⊙⊙⊙⊙⊙
2010 ⊙⊙⊙⊙⊙⊙⊙
2009 ⊙⊙⊙
⊙ = 100,000 CDs
10) Using the pictograph, how many more CDs were projected to be sold during the band's best projected
year versus their least projected sales year?
Use the circle graph to solve the problems.
11) A survey of the 5417 vehicles on the campus of State University yielded the following circle graph. Find the
number of vans. Round your result to the nearest whole number.
11%
14%
35%
8%
3%
29%
12) Referring to the circle graph, how many more hatchbacks are there than convertibles?
2
13) Referring to the circle graph, which vehicle showed up the least in the survey? How many of that vehicle
were there?
Use the graph to answer the questions.
Big "D" Sales (2008-2009)
2009
Sales
(Thousands of $)
2008
Month
14) Which month in 2008 had the lowest sales?
15) Which month in 2009 had the highest sales?
16) What was the increase in sales between month 5 and month 6 of 2009?
17) What were the total sales for the first 6 months of 2009?
18) What were the total sales for 2008?
19) What was the total increase in sales from 2008 to 2009?
20) What was the difference between the highest and lowest monthly sales in 2008?
3
21) The histogram below shows the efficiency level (in miles per gallon) of 110 cars. How many cars have an
efficiency between 15 and 20 miles per gallon?
22) Using the histogram, determine how many cars have an efficiency of more than 20 miles per gallon.
23) Using the histogram, determine the percentage of cars that have an efficiency of less than 20 miles per
gallon. Round your answer to the nearest tenth of a percent.
4
Answer Key
Testname: DMA-050 WORKSHEET 1
1) 200
2) approximately 1250
3) English
4) Science
5) 50
6) approximately 250 students
7) 8
8) $25,500
9) Between 2014 and 2015
10) $800,000
11) approximately 433 vans
12) approximately 1138 more hatchbacks than convertibles
13) sedans, approximately 163
14) Month 3
15) Month 12
16) $4000
17) $366,000
18) $582,000
19) $182,000
20) $8000
21) 35
22) 40
23) approximately 63.6%
5
DMA 50 Worksheet #2
The Rectangular Coordinate System, Graphing Linear Equations, and Intercepts
Show your work. If the problem is a real world
application or "word problem", write a complete
sentence as your final answer.
4) A(0, -2), B (0, 5)
y
Plot the ordered pairs on the rectangular coordinate
system provided.
1) A(1, 3), B(-2, 4)
y
6x
6x
5) A(5, 0), B (-4, 0)
y
2) A(-3, -3), B(-5, 2)
y
6x
6x
List the quadrant(s) in which the given point is located.
6) (4, 2)
7) (-13, 16)
3) A(4, 1), B(1, -3)
y
8) (-15, -14)
9) (3, -19)
10) (-18, 0)
6x
11) The first coordinate is positive.
12) The second coordinate is negative.
13) The coordinates have the same sign.
1
Graph the linear equation by creating a table and
finding ordered pairs.
14) y = 3x + 2
Find the x- and y-intercepts for the equation. Use a table
to create the ordered pairs. Then graph the equation.
17) x + 3y = 6
y
y
-10
15) y =-
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
5
10 x
5
10 x
5
10 x
18) 4x - 20y = 20
1
x-3
5
y
10
y
10
5
5
-10
-10
-5
5
-5
10 x
-5
-5
-10
-10
19) -6x - 30y = 30
y
16) -x + 7y = 7
10
y
10
5
5
-10
-10
-5
5
10 x
-5
-5
-5
-10
-10
2
Graph the horizontal or vertical line.
20) y = 2
23)
y
10
y
10
5
10 x
-10
-10
-5
5
10 x
-5
-10
-10
21) x = -1
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
Write an equation for the graph.
22)
y
10
5
-10
-5
-5
-10
3
Answer Key
Testname: DMA-050 WORKSHEET 2 PART 1 OF 2
1)
y
B
A
6x
2)
y
B
6x
A
3)
y
A
6x
B
4)
y
B
6x
A
4
Answer Key
Testname: DMA-050 WORKSHEET 2 PART 1 OF 2
5)
y
B
A
6x
6) I
7) II
8) III
9) IV
10) On an axis
11) I, IV
12) III, IV
13) I, III
14)
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
15)
y
10
5
-10
-5
-5
-10
5
Answer Key
Testname: DMA-050 WORKSHEET 2 PART 1 OF 2
16)
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
17) 6, 0 , 0, 2
y
10
5
-10
-5
-5
-10
18) (0, -1), (5, 0)
y
10
5
-10
-5
-5
-10
6
Answer Key
Testname: DMA-050 WORKSHEET 2 PART 1 OF 2
19) (0, -1), (-5, 0)
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
20)
y
10
5
-10
-5
-5
-10
21)
y
10
5
-10
-5
-5
-10
22) x = 4
23) y = 2
7
24) Greg’s cell phone plane charges a fixed monthly fee, plus an amount for each minute over the number of
minutes included with the plan. Last month, Greg went over by 38 minutes, and the bill was $57.10. This
month, Greg went over by 84 minutes and the bill was $77.80.
a. Fill in the following chart using the information above.
x = Number of Minutes Over y = Total Bill
38
84
b. Write two ordered pairs using the information above.
c. Label the grid and axis, then plot the two ordered pairs below. Use a straight edge or ruler to connect the
two points. Extend the line until it crosses the y-axis.
d. What was the total bill when Greg exceeded the plan by 38 minutes?
e. What was the total bill when he exceeded the plan by 84 minutes?
f. What would the total bill have been if Greg did not exceed his minute limit? Hint: 0 minutes
g. What would the total bill have been if he exceeded the plan by 50 minutes?
h. How many minutes did he go over if the bill was $94.00?
1
25) The hourly wage y of an employee at a certain production company is given by y = .25x + 9 , where x is the
number of units produced by the employee in an hour.
a . Complete the table.
x (# of units made) y (hourly wage)
5
10
20
b. Label and graph the equation.
c. Find the number of units that an employee must produce each hour to earn an hourly wage of $12.25. Use
the graph to make an estimate (prediction) and then use the equation to find the answer mathematically.
d. If the employee does not make any units, how much money does he/she make? In your opinion, does
this seem fair?
2
26) The cost y, in dollars, for a company to produce x computer desks is given by y = 80x + 5000.
a. Complete the table below.
x (# of computers)
y (cost)
10
15
20
b. Label and graph the equation.
c. Use the graph to find the number of computer desks that can be produced for $8600.00.
d. Use the equation to find the number of computer desks that can be produced for $8600.00
e. Does it still cost the company money if no computer desks are made? If so how much?
3
Answer Key
Testname: DMA-050 WORKSHEET 2 PART 2 OF 2
24) a. $57.10, $77.80 b.(38,57.10),(84,77.80) c.Graph d.$57.10 e.$77.80 f. approx $40.00 g. approx $62.50 h. approx 120 min
25)a. $10.25, $11.50, $14.00 b. Graph c. approx 13 units d. $9.00/hour,opinions may vary
26) a. $5800, $6200, $6600 b. Graph c. approx 45 computers d. 45 computers e. yes, $5000
4
DMA 50 Worksheet #3
Slope
Show your work. If the problem is a real world application or "word problem", write a complete sentence as your
final answer.
Find the slope of the line.
1)
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
2)
y
10
5
-10
-5
-5
-10
3)
y
10
5
-10
-5
-5
-10
1
4)
y
10
10 x
-10
-10
Graph the line containing the given pair of points and find the slope.
5) (2, -8) (-1, 4)
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
6) (6, -3) (3, 7)
y
10
5
-10
-5
-5
-10
Find the slope of the line going through the pair of points.
7) (8, 6), (-6, -9)
2
8) (1, 9), (7, -9)
9) (6, 5), (-4, 5)
10) (-9, -9), (-9, -7)
Find the slope of the line.
11) 2x - 3y = 10
12) y = 2 x - 6
3
13) 3x + 4y = 21
14) -4y = -2x - 18
15) x = -1
16) y = -4
Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
17) 3x - 4y = 4
8x + 6y = 4
18) 6x + 2y = 8
9x + 3y = 14
3
19) y = 2x - 4
6x + 3y = 8
Solve the problem.
20) Kannanaski Rapids drops 64 ft vertically over a horizontal distance of 811 ft. What is the slope of the rapids?
21) Over one particular stretch of road, the Whitepoint Highway rises 495 ft over a horizontal distance of 3400 ft.
Find the grade of the road.
Find the slope (or rate of change). Use appropriate units.
22) Find the slope (or pitch) of the roof.
2.8 ft
7.1 ft
Solve the problem.
23) The following graph shows data for a recent train ride from New York to Toronto. Find the rate of change of
the distance from New York with respect to time, in miles per hour.
200
100
1
2
3
4
5
Time of Day (PM)
4
24) The value of a particular car is represented in the following graph. Find the rate of change of the value of the
car with respect to time, in dollars per year.
v
20000
19000
18000
17000
16000
1998 1999 2000 2001 2002
t
25) The value of a particular computer system is represented in the following graph. Find the rate of change of
the value of the computer system with respect to time, in dollars per year.
v
4
3.5
3
2.5
2
1.5
1
0.5
1
2
3
4
5
6
Time from purchase (in years)
7
8 t
26) Find the rate of change. Use appropriate units.
80
y
70
60
50
40
Distance
Traveled
in Miles
30
20
10
1
2
3
4
5 x
Number of Hours Spent Traveling
5
27) Find the rate of change. Use appropriate units.
y
30
25
20
Value of
Car in
Thousands
of Dollars
15
10
5
1
2
3
4
5
x
Number of Years of Use
6
Answer Key
Testname: DMA-050 WORKSHEET 3
1)
1
4
2) -1
3) Undefined
4) 0
5) - 4
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
6) -
10
3
y
10
5
-10
-5
-5
-10
7)
15
14
8) - 3
9) 0
10) Undefined
2
11)
3
12)
13) 14)
3
4
1
2
15) Undefined
16) 0
17) Perpendicular
7
Answer Key
Testname: DMA-050 WORKSHEET 3
18) Parallel
19) Neither
20) -0.079
21) 14.6%
22) 39.4%
23) 60 miles per hour
24) -$700 per year
25) -$250 per year
26) 5.0 miles per hour
27) -$4,000 per year
8
DMA 50 Worksheet #4
Equations of Lines
Show your work. If the problem is a real world application or "word problem", write a complete sentence as your
final answer.
Graph using the slope and the y-intercept.
1) y = x - 6
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
2) y = -
6
x- 2
5
y
10
5
-10
-5
-5
-10
3) x -2y = 4
y
10
5
-10
-5
-5
-10
1
4) 2x - y = 6
y
10
5
-10
-5
5
10 x
-5
-10
Find an equation of the line with the given slope and y-intercept. Write the equation in slope intercept form
(y=mx+b) and in standard form (Ax+By=C).
5) Slope = 8 , y-intercept = (0, -5)
5
6) Slope = -4.7, y-intercept = (0, 3.05)
Find an equation of the line containing the given point and having the given slope. Write the equation in
slope-intercept form and standard form.
7) (4, 5), m = - 2
8) (3, 4), m = - 2
9
Find an equation of the line that contains the given pair of points. Write the equation in the form y = mx + b and
Ax+By=C.
9) (-4, 0) and (0, -5)
10) (-4, -8) and (3, -2)
2
11) (9, 7) and (9, -10)
12) (3, -3) and (-10, -3)
The next three problems are equations of horizontal or vertical lines. Write the equation in the form of y = # or x = #.
13) (-7, -10), m = 0
14) (-6, 5) and (-6, 9)
15) (-10, 10) and (5, 10)
Write an equation of the line described. Write the equation in the form of y = mx + b and Ax + By = C.
16) Through (-5, -2), parallel to 3x + 5y = 5
17) Through (-3, -8), perpendicular to -8x + 7y = 80
18) Through (-9, -4), perpendicular to x = 7
Solve the problem.
19) Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales
were $14,000 in 1982 and $77,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales y.
20) Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that
exam. Persons taking a 70-hour review course average a score of 792. Find a linear function S(t), which fits
this data, and which expresses score as a function of time.
3
21) A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon,
whereas they sell 3884 gallons on a day that they charge $1.40 per gallon. Find a linear function that
expresses gallons sold as a function of price. Use this function to predict the number of gallons sold at a price
of $1.24 per gallon.
22) The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the
total sales after 30 months.
4
Answer Key
Testname: DMA-050 WORKSHEET 4
1)
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
y
10
5
-10
-5
-5
-10
2)
3)
y
10
5
-10
-5
-5
-10
5
Answer Key
Testname: DMA-050 WORKSHEET 4
4)
y
10
5
-10
-5
5
10 x
-5
-10
5) y = 8 x - 5
5
6) y = -4.7x + 3.05
7) y = -2x + 13
2
14
8) y = - x +
9
3
9) y = 10) y =
5
x- 5
4
6 - 32
x
7
7
11) x = 9
12) y = -3
13) y = -10
14) x = -6
15) y = 10
3
16) y = - x - 5
5
17) y = -
7 - 85
x
8
8
18) y = -4
19) S(x) = 12,600x + 14,000
20) S(t) = 4.3t + 491
21) 6879.19982 gallons
22) $83,050
6
DMA 050 Review
Show your work. If the problem is a real world application or "word problem", write a complete sentence as your
final answer.
Use the pictograph to answer the question.
1) This pictograph shows projected sales of compact disks (CDs) for a popular rock band for seven consecutive
years.
Approximately how many fewer CDs will be sold in 2007 than in 2010?
Year Projected CD Sales
2013 ⊙⊙
2012 ⊙⊙⊙⊙⊙⊙
2011 ⊙⊙⊙⊙⊙⊙⊙⊙⊙
2010 ⊙⊙⊙⊙⊙⊙⊙⊙⊙⊙
2009 ⊙⊙⊙⊙⊙
2008 ⊙⊙⊙⊙⊙⊙⊙
2007 ⊙⊙⊙
⊙ = 10,000 CDs
2) Using the pictograph above, which year is projected for having the least sales?
3) How many total CDs are projected to be sold in 2010, 2011, 2012, and 2013?
The bar graph below represents various colors of cars sold. Use the graph to answer the question(s).
4) Estimate the number of red cars sold.
5) Estimate how many more tan cars were sold than yellow cars.
6) Which color sold the closest to 30,000 cars?
1
The line graph below shows the price of a stock over the course of the day. Use the graph to answer the question(s).
Stock Price
(in dollars)
9
8
7
6
5
4
3
2
1
9AM 10AM 11AM 12PM 1PM 2PM 3PM 4PM 5PM 6PM
7) At what time was the stock price the lowest?
8) What happened between 11am and 12pm? Did this happen between two consecutive time intervals at any
other time during the day?
9) What is the difference between the opening stock price (9am) and the closing stock price (6pm)?
Use the circle graph to solve the problem.
10) The circle graph shows the percent of the total population of 45,400 of Springfield living in the given types of
housing.
40%
31%
2%
8%
19%
Find the number of people who live in single family houses. Round your result to the nearest whole number.
2
Find the slope of the line.
11)
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
12)
y
10
5
-10
-5
-5
-10
Find the slope of the line containing the two given points.
13) (14, -11) and (-19, 18)
Find the slope of the line.
14) 2x + 5y = 26
3
Find the slope (or rate of change). Use appropriate units.
15)
y
40
35
Value of
Car in
Thousands
of Dollars
30
25
20
15
10
5
1
2
3
4
5
6
x
Number of Years of Use
Graph the equation by determining the missing values needed to plot the ordered pairs.
16) x - 2y = -6;
Fill in the missing values of the four ordered pairs below. Plot these four points and sketch the line.
(0, ), ( , 0), (2, ), ( , 2)
y
10
5
-10
-5
5
10 x
-5
-10
4
Graph using any technique of your choice.
2
17) y = x - 5
5
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
Graph.
18) y = -2
y
10
5
-10
-5
-5
-10
Graph using any technique of your choice.
19) x + 4y = 16
y
10
5
-10
-5
5
10 x
-5
-10
Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
20) 6x + 2y = 8
15x + 5y = 21
5
Write an equation for the line described. Give your answer in standard form. That is, Ax + By = C .
21) through (0, 3), m = 2
3
Write an equation for the line described. Give your answer in slope-intercept form. That is y = mx + b .
22) m = -9, through (-7, 4)
Find an equation of the line that contains the given pair of points. Write the equation in the form y = mx + b.
23) (6, 2) and (3, 0)
Write an equation for the line described. Write the equation in the form specified.
24) perpendicular to 2x - 5y = 50, through (5, 8); standard form
Solve the problem.
25) The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the
total sales after 45 months.
6
Answer Key
Testname: DMA 50 REVIEW
1) 70,000 CDs
2) 2013
3) 270000 CDs
4) 60,000
5) 20,000
6) Tanx
7) 9am
8) The stock price remained the same. This also happened from 4pm to 5pm.
9) $3.00
10) 18,160 people
1
11)
4
12) Undefined
29
13) 33
14) -
2
5
15) -$2000 per year
16)
y
10
5
-10
-5
10 x
5
-5
-10
y
10
5
-10
-5
5
10 x
-5
-10
17)
7
Answer Key
Testname: DMA 50 REVIEW
18)
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
19)
y
10
5
-10
-5
-5
-10
20) Parallel
21) 2x - 3y = -9
22) y = -9x - 59
2
23) y = x - 2
3
24) 5x + 2y = 41
25) $115,300
8