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Graphs and Solving Linear Equations Word Problems (20 Problems)

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Solve the following equations for the unknown.

1. 5x = 20

2. 7x - 3 = 18

Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph.

3. y = x + 3

4. y = -2x - 7

5. 2x + 3y = 9

6.
A consumer electronics company sells 6.7 million MP3 players per month at a price of $100 apiece; when the price is lowered to $80, the company sells 10.2 million players per month. How many MP3 players can the company expect to sell per month at a price of $75?

7.
The points (1,5), (4,5), and (1,0) represent three corners of a rectangle; find the coordinates of the fourth point.

8.
Seven inches are equivalent to 17.78 cm. Find the equation converting length in cm to length in inches. What is the length in inches of a 96.2 cm bar?

9.
Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).

10.
Sales tax in Pennsylvania is 6%. Create an equation for the total price (cost plus tax) of a purchase in PA in terms of its cost. How much would a person pay for a car whose cost is $32,000?

11. 6.2(x - 15.1) = 9.3(-x - 3.2)

12. x/3 - 7/8 = 2/5(x + 15/4)

Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph.

13. 7.1x - 3.9y = 1.4

14. 3x = -2

15.. 4.2x + 3.8y = 1.9

16.
A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?

17.
Find the area of a rectangle if three of its corners are (-0.1,-3.4), (-7.9,-3.4), and (-0.1,6.8).

18.
A temperature of 41 degrees F is equivalent to 278.2 degrees K, while a temperature of 86 degrees F is equivalent to 303.2 degrees K. Find the equation converting Kelvin temperature to Fahrenheit. What is the Fahrenheit temperature when it is 180 degrees K?

19.
Find an equation in slope-intercept form passing through the points (-6.2,18.1) and (-3.4,18.1).

20.
Tom buys $20,000 worth of stock, and sells it eight months later for $28,000. If he is required to pay 15% capital gains tax on his profits, how much tax will he pay?

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Solution Summary

Graphs and Solving Linear Equations are investigated. The solution is detailed and well presented.

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Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.

Complete and please show all the work.
Please see attached file for full problem description.

1. List all the factors of 45.

2. Which number is prime?
A) 1
B) 12
C) 31
D) 99

3. List all the prime numbers between 25 and 60.

4. Find the GCF for 68, 85, and 153.

5. Find the LCM for 18 and 27.

6. Multiply and write the result in simplest form.

A)

B)

C)

D)

7. Add.

8. Subtract. -

9. Evaluate. (3 ? 2 + 1)2

10. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2) - 2]
A) 10
B) 1
C)

D) 8

11. Evaluate. | -48 |

12. Write the following phrase using symbols. Use the variable x to represent the number.
A number decreased by by 6

13. Subtract. -11 - 20
A) 31
B) -9
C) 9
D) -31

14. Divide.

A) -6
B) 0
C) undefined
D) 1

15. Combine like terms.
2r + 10s + 4r
A) 6r + 10s
B) 16rs
C) 12r + 4s
D) 16r + s

16. Divide.

A) m2n3
B) m4n4
C) m2n4
D) m4n3

17. Multiply.
a7 a5

18. Solve. x - 9 = -6

19. Solve. 10x - = 9x +

A)

B)

C)

D)

20. Solve. 8x - 11 = 2x + 1

21. Translate the following statement into an algebraic equaion. Let x represent the number.
3 more than 9 times a number is 4 times that same number.

22. Solve. 8 - (4x - 3) = 19

23. Tickets for a play at the community theater cost $14 for an adult and $2 for a child. If 270 tickets were sold and the total receipts were $2340, how many of each type of ticket were sold?

24. Graph the solution set of x  -1.
A)
-1 0
B)
-1 0
C)
-1 0
D)
-1 0

25. Solve and graph the solution set. 3x  7x + 20
A)
-5 0
B)
-5 0
C)
0 5
D)
0 5

26. Which of the ordered pairs is a solution for the equation 4x - 3y = 12?
A) (0, 4)
B) (-3, 0)
C) (-3, -4)
D) (0, -4)

27. Plot the point with coordinates (-4, 3).
A)

B)

C)

D)

28.
Graph 3x + y = 3.

29. Graph y = 4.

30. Find the slope of the line passing through the points (0, 2) and (-10, 9).
A)

B)

C)

D)

31. Find the slope of the line passing through the points (-2, 2) and (-2, -3).
A) 0
B) 1
C) -5
D) Undefined

32. Find the slope of the graphed line.

A) 2
B) -2
C)

D) -

33. The following pie chart represents the eye color of students in a certain class.

What percentage of students in the class had blue or brown eyes?

34. The line graph below shows the number of trees in a certain seaside town.

(a) Which year had the fewest trees?

(b) Between which two years did the greatest increase in the number of trees occur?

35. Find the slope and y-intercept.
-9x - 8y = -64

36. Find the slope.
7x + 2y = -11

37. Match the graph with one of the equations.

A)

B)

C) y = -3x + 1
D) y = 3x + 1

38. A roof rises 2.75 ft over a horizontal distance of 10.69 ft. What is the slope of the roof to the nearest hundredth?
A) 3.89
B) 0.26
C) 1.60
D) 2.77

39. Determine which two equations represent parallel lines.
(a) y = 5x - 10 (b) y = -5x + 10 (c) y = 5x + 5 (d) y = x - 10

40. Graph the inequality.
y  3x

41. Rewrite the equation 2x - 3y = -6 as a function of x
A)

B)

C)

D)

42. Solve the system by graphing.
x - 2y = 8
x + y = -1

43. Solve the system by addition.
x + y = 1
x - y = 9

44. Solve the system by addition.
-4x + 5y = 5
x - 2y = -2

45. The sum of two numbers is 43. The second is 1 more than 2 times the first. What are the two numbers?

46. Solve the following system of linear inequalities by graphing.
x + 2y  3
2x - 3y  6
A)
B)
C)
D)

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