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Graphing Linear Equations Practice Problems

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Updated on Aug 24, 2011

To review these concepts, go to Graphing Linear Equations Study Guide.

Practice

Using graph paper, plot the following points. You can plot all of these points on the same coordinate plane.

  1. (8,2)
  2. (8,–2)
  3. (0,4)
  4. (5,0)
  5. (–5,–5)
  6. (–1,5)
  7. (6,–3)
  8. (–6,–2)
  9. (2,9)
  10. (–7,3)

Find the slope (m) and y-intercept (b) of each equation.

  1. y = 3x + 9
  2. y = 5x – 6
  3. y = –5x + 16
  4. y = 2x + 3
  5. y = 2x+ 4
  6. y = 5x – 2
  7. y = –2x + 9
  8. y = –2.3x – 7.5
  9. (Hint: The number in front of the x is 1.)

Change the equations into slope-intercept form. Then state the slope (m) and y-intercept (b).

  1. 9x – 6y = 12
  2. –30x + 15y = 15
  3. 18x – 12y = 48
  4. 7y + 14x = 21
  5. 4y – 48x = 36
  6. 100x – 10y = 50
  7. –24x – 24y = 24
  8. y = –18

Use graph paper to graph these linear equations.

  1.   y = x + 4  
  2. y = 2x + 3  
  3. y = 3x – 2  
  4. y = –2x + 5  
  5.  
  6.  
  7.  
  8. –8x + 4y = –12  
  9. 4x + 4y = 12  
  10. –8x + 4y = 8  
  11. –5x + 10y = 20  
  12. –4x + 3y = 12  
  13. x + y – 3 = 0  
  14. –3x + 4y = 12

Applications Practice

  1. On a slanted bridge, cars ascend 70 ft. for every 700 ft. traveled horizontally. What is the slope of the line that represents the bridge's incline?
  2. You are a sales clerk in a clothing store. You receive a salary of $320 per week plus a 5% commission on all sales. Write an equation to represent your weekly salary. (Let y equal the weekly salary and x equal the amount of sales.) What are the slope and y-intercept of your equation?
  3. You are renting a car. It will cost you $25 per day plus $0.10 per mile per day. Write an equation to represent the daily cost of renting the car. What are the slope and y-intercept of your equation?
  4. A phone plan charges $5 a month plus $0.05 for every minute used each month. Write an equation to represent the total monthly cost of the phone plan. Graph the linear equation.
  5. When you travel at a speed of 60 mph, write an equation that represents how far you will travel in x hours. Then graph the linear equation. (When you set your scale on your graph, let each unit represent 1 hour on the x scale and 10 miles on the y scale. You can use different scales on the x- and y-axes so that your graph is a reasonable size.)

Solutions

1–10.

 

Graphing Linear Equations

  1. m = 3, b = 9
  2. m = 5, b = –6
  3. m = –5, b = 16
  4. m = 2 , (0,3)
  5. m = 5 , (1,3)
  6. m = –2 , (1,7)
  7. m = 2 , (1,6)
  8. m = –2.3, b = –7.5
  9. y = 2x + 1, m = 2, b = 1
  10. y = –10x + –8, m = –10, b = –8
  11. y = x + 18, m = 1, b = 18
  12. y = –2x + 3, m = –2, b = 3
  13. y = 12x + 9, m = 12, b = 9
  14. y = 10x + 5, m = 10, b = –5
  15. y = –x + 1, m = –1, b = –1
  16. y = –18, m = no slope, b = –18
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  31. y = 0.10x + 25, m = 0.10, b = 25
  32. y = 0.05x + 5   Graphing Linear Equations
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    Graphing Linear Equations
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