Linear Equations and Inequalities: Get Stronger Answer Key

Graphing and Analyzing Linear Equations

  1. The x-intercept is [latex](2, 0)[/latex] and the y-intercept is [latex](0, 6)[/latex].
  2. The x-intercept is [latex](2, 0)[/latex] and the y-intercept is [latex](0, -3)[/latex].
  3. The x-intercept is [latex](3, 0)[/latex] and the y-intercept is [latex](0, \frac{9}{8})[/latex].
  4. [latex]y = 4 - 2x[/latex]
  5. [latex]y = \frac{5 - 2x}{3}[/latex]
  6. [latex]y = 2x - \frac{4}{5}[/latex]
  7. [latex]d = \sqrt{74}[/latex]
  8. [latex]d = \sqrt{36} = 6[/latex]
  9. [latex]d \approx 62.97[/latex]
  10. [latex]\left( 3, -\frac{3}{2} \right)[/latex]
  11. [latex]\left( 2, -1 \right)[/latex]
  12. [latex](0, 0)[/latex]
  14. [latex]y = 0[/latex]
  15. not collinear
  16. [latex]A: (-3, 2), B: (1, 3), C: (4, 0)[/latex]
  17. [latex]x[/latex] [latex]y[/latex]
    [latex]-3[/latex] [latex]1[/latex]
    [latex]0[/latex] [latex]2[/latex]
    [latex]3[/latex] [latex]3[/latex]
    [latex]6[/latex] [latex]4[/latex]

  18. [latex]x[/latex] [latex]y[/latex]
    [latex]-3[/latex] [latex]0[/latex]
    [latex]0[/latex] [latex]1.5[/latex]
    [latex]3[/latex] [latex]3[/latex]

  20. [latex]d = 8.246[/latex]
  22. [latex]d = 5[/latex]
  24. [latex](-3, 4)[/latex]
  26. [latex]m = -\frac{9}{7}[/latex]
  28. [latex]m = \frac{3}{2}[/latex]

Equations of Lines

  1. [latex]x = 2[/latex]
  2. [latex]x = \frac{2}{7}[/latex]
  3. [latex]x = 6[/latex]
  4. [latex]x = 3[/latex]
  5. [latex]x = -14[/latex]
  6. [latex]x \neq -4; x = -3[/latex]
  7. [latex]x \neq 1;[/latex] when we solve this we get [latex]x = 1[/latex], which is excluded, therefore NO solution
  8. [latex]x \neq 0; x = -\frac{5}{2}[/latex]
  9. [latex]y = \frac{4}{5}x + \frac{14}{5}[/latex]
  10. [latex]y = \frac{3}{4}x + 2[/latex]
  11. [latex]y = \frac{1}{2}x + \frac{5}{2}[/latex]
  12. [latex]y = -3x - 5[/latex]
  13. [latex]y = 7[/latex]
  14. [latex]y = -4[/latex]
  15. [latex]8x + 5y = 7[/latex]
  16. Parallel
  17. Perpendicular

Modeling with Linear Equations

  1. [latex]2,000 - x[/latex]
  2. [latex]v + 10[/latex]
  3. [latex]\text{Ann: } 23; \text{Beth: } 46[/latex]
  4. [latex]20 + 0.05m[/latex]
  6. [latex]300[/latex] min
  8. [latex]90 + 40P[/latex]
  10. [latex]6[/latex] devices
  12. [latex]50,000 - x[/latex]
  14. [latex]4[/latex] h
  15. She traveled for [latex]2[/latex] hours at [latex]20[/latex]mi/h, or [latex]40[/latex] miles.
  16. [latex]\$5,000 \text{ at 8% and } \$15{,}000 \text{ at 12%}[/latex]
  18. [latex]B = 100 + 0.05x[/latex]
  20. Plan A
  21. [latex]R = 9[/latex]
  22. [latex]r = \frac{4}{5} \text{ or } 0.8[/latex]
  24. [latex]W = \frac{P - 2L}{2} = \frac{58 - 2(15)}{2} = 14[/latex]
  26. [latex]f = \frac{pq}{p + q} = \frac{8(13)}{8 + 13} = \frac{104}{21}[/latex]
  28. [latex]m = - \frac{5}{4}[/latex]
  30. [latex]h = \frac{2A}{b_1 + b_2}[/latex]
  32. [latex]\text{length} = 360 \, \text{ft}; \, \text{width} = 160 \, \text{ft}[/latex]
  34. [latex]405 \, \text{mi}[/latex]
  36. [latex]28.7[/latex]
  38. [latex]h = \frac{V}{\pi r^2}[/latex]
  40. [latex]r = \sqrt{\frac{V}{\pi h}}[/latex]
  42. [latex]C = 12\pi[/latex]

Linear Inequalities

  1. [latex]14 + 7i[/latex]
  2. [latex]-\frac{23}{29} + \frac{15}{29}i[/latex]
  6. [latex]2 - \frac{2}{3}i[/latex]
  8. [latex]4 - 6i[/latex]
  10. [latex]128i[/latex]
  11. [latex]\left( \frac{\sqrt{3}}{2} + \frac{1}{2}i \right)^6 = -1[/latex]
  12. [latex]3i[/latex]
  13. [latex]0[/latex]
  14. [latex]5 - 5i[/latex]
  15. [latex]-2i[/latex]