Practice Problems for 
Linear equations and graphs


A. Solve each of the following equations, and check each result.  (Answers)

1. 5x - 8 = 17 11. 2 (2x - 1) = 3 (x + 1) 
2. 8 - 7x = -41 12. 8x - 3(2x - 4) = 17 
3. 7x - 5 = 6x + 6 13. 7 (3x + 4) = 8 (2x + 5) + 13 
4. 8x - 4 = 3x - 24 14. 9 - 4 (3x + 1) = 3 (6 - 3x) - 9 
5. 7x - 4 = 2x + 26 15. 2x/3 - 5/3 = 3 
6. 4x - 3 = 1 - 2x  16. x/6 + x/5 = 11 
7. 2x + 8 = 7x - 37  17. 2x/3 - x/4 = 5/2 
8. 6x + 5 = 8x - 10  18. x/5 - (x - 7)/3 = 1/3 
9. 5x = 3(x - 6)  19. 0.5 x - 6 = 0.2 x 
10. 5 (8 - x) = 3x  20. 0.15 x + 1.2 = 0.05 x + 2 

B. For each of the following equations, find the x- and y-intercepts, sketch the line and find the slope of the line.  (Answers)

1. x - 2y = 4
2. x + 3y = 6
3. x/3 - y/6 = 1
4. x/4 + y/6 = 1
5. 2x + 5y = 10
6. 2x - 3y = 6
7. x + 4y + 8 = 0
8. 2x - y + 6 = 0

C. Find an equation of the line which passes through each of the following pairs of points. Sketch the line labeling the x- and y-intercepts and find the slope of the line.  (Answers)

1. The points (2,3) and (4,7)
2. The points (2,-3) and (-2,-5)
3. The points (2,5) and (-3,5)
4. The points (-1,4) and (-1,7)
5. The points (8,-3) and (-2,-5)
6. The points (-4,-3) and (2,-7)

Answers

A. The solutions for x

1. 5
2. 7
3. 11
4. -4
5. 6
6. 2/3
7. 9
8. 15/2
9. -9
10. 5
11. 5
12. 5/2
13. 5
14. -4/3
15. 7
16. 30
17. 6
18. 15
19. 20
20. 8

B. Everything but the graphs

1. (4,0), (0,-2), slope is 1/2
2. (6,0), (0,2), slope is -1/3
3. (3,0), (0,-6), slope is 2
4. (4,0), (0,6), slope is -3/2
5. (5,0), (0,2), slope is -2/5
6. (3,0), (0,-2), slope is 2/3
7. (-8,0), (0,-2), slope is -1/4
8. (-3,0), (0,6), slope is 2

C. Just the equations of the lines

1. y - 3 = 2 (x - 2)
2. y + 3 = 1/2 (x - 2)
3. y = 5
4. x = -1
5. y + 3 = 1/5 (x - 8)
6. y + 3 = -2/3 (x + 4)

 
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