8. Review Exercises

Answers to the odd-numbered questions are available at the end of the book.

1. In which quadrant or on which axis do the following points lie?
   a. A (5, −1)
   b. B (−2, 3)
   c. C (3, 0)
   d. D (4, −2)
   e. E (2, 0)
   f. F (0, 4)
2. In which quadrant or on which axis do the following points lie?
   a. A (4, −1)
   b. B (−5, 0)
   c. C (−2, −7)
   d. D (0, −3)
   e. E (6, 6)
   f. F (5, 4)
3. Plot the following points and join them in the order A, B, C, D. Identify the type of quadrilateral and find its area and perimeter.
   a. A (6, −3)
   b. B (6, −6)
   c. C (−2, −6)
   d. D (−2, −3)
4. Plot the following points and join them in the order P, Q, R, S. Identify the type of quadrilateral and find its area and perimeter.
   a. P (–2, 4)
   b. Q (–8, 4)
   c. R (–8, –2)
   d. S (–2, –2)

For problems 5 to 10, graph the equations using a table of values with four points.

5. [latex]4x - y = 2[/latex]
6. [latex]2x + 3y = 12[/latex]
7. [latex]x + y - 4 = 0[/latex]
8. [latex]x + 2y - 4 = 0[/latex]
9. [latex]\displaystyle{y = \frac{1}{2}x + 2}[/latex]
10. [latex]\displaystyle{y = -\frac{1}{2}x - 2}[/latex]

For problems 11 to 16, graph the equations using the x-intercept, y-intercept, and another point.

11. [latex]3x - 4y = 12[/latex]
12. [latex]x - 2y = -1[/latex]
13. [latex]x - 2y - 6 = 0[/latex]
14. [latex]3x + y - 4 = 0[/latex]
15. [latex]y = 4x[/latex]
16. [latex]x = 2y[/latex]

For problems 17 to 22, graph the equations using the slope and y-intercept method.

17. [latex]y = 4x + 6[/latex]
18. [latex]y = 5x + 4[/latex]
19. [latex]3x + 2y - 12 = 0[/latex]
20. [latex]2x + 3y + 6 = 0[/latex]
21. [latex]\displaystyle{y = -\frac{3}{4}x - 1}[/latex]
22. [latex]\displaystyle{y = -\frac{1}{3}x - 1}[/latex]

For problems 23 to 28, determine the equation of the line in slope-intercept form that passes through the following points:

23. (3, 2) and (7, 5)
24. (4, 6) and (2, 4)
25. (5, –4) and (–1, 4)
26. (0, –7) and (–6, –1)
27. (1, –2) and (4, 7)
28. (3, –4) and (–1, 4)

29. Write the equation of a line parallel to [latex]3x - 4y = 12[/latex] and that passes through the point P(−2, 3).
30. Write the equation of a line parallel to [latex]x - 3y = 9[/latex] and that passes through the point P(2, –3).
31. Write the equation of a line perpendicular to [latex]2y = x + 4[/latex] and that passes through the point P(–2, 5).
32. Write the equation of a line perpendicular to [latex]3x + 4y + 6 = 0[/latex] and that passes through the point P(4, –1).