Linear Functions: Get Stronger Answer Key

Introduction to Linear Functions

  1. Yes
  2. Yes
  3. No
  4. Yes
  5. Increasing
  6. Decreasing
  7. Decreasing
  8. Increasing
  9. Decreasing
  10. [latex]2[/latex]
  11. [latex]-2[/latex]
  12. [latex]g(x)=-3x+5[/latex]
  13. [latex]f(x)=5x-5[/latex]
  14. [latex]g(x)=-\dfrac{25}{2}x+6[/latex]
  15. [latex]f(x)=10x-24[/latex]

Graphs of Linear Functions

  1. [latex]y=\dfrac{3}{5}x-1[/latex]
  2. [latex]y=3x-2[/latex]
  3. [latex]y=-\dfrac{1}{4}x+\dfrac{11}{3}[/latex]
  4. [latex]y=-1.5x-3[/latex]
  5. perpendicular
  6. parallel [latex]f(0)=-(0)+2[/latex] [latex]f(0)=2[/latex]
  7. Line 1: [latex]m=-10[/latex] Line 2: [latex]m=-10[/latex] Parallel
  8. Line 1: [latex]m=-2[/latex] Line 2: [latex]m=1[/latex] Neither
  9. Line 1: [latex]m=-2[/latex] Line 2: [latex]m=-2[/latex] Parallel
  10. [latex]y=3x-3[/latex]
  11. [latex]y=-\dfrac{3}{3}t+2[/latex]
  12. [latex]y=-\dfrac{5}{4}x+5[/latex]
  13. [latex]y=3x-1[/latex]
  14. [latex]y=-2.5[/latex]
  15. F
  16. C
  17. A
  18. Graph of f with an x-intercept at -4 and y-intercept at -2 which gives us a slope of: 2.
  19. Graph of f with an y-intercept at 3 and a slope of 2/5.
  20. Graph of a line that passes through the points (-3, -4) and (3, 0) which results in a slope of 2/3.
  21. Graph of g(x) = -3x + 2 which goes through the points (0,2) and (1,-1) with a slope of -3.
  22. Graph of k(x) = . This line goes through the points (0,-3) and (3,-1) and has a slope of 2/3.
  23. Graph of the line p(t) = 3t -2. This line goes through the points (0,-2) and (1,1) which has a slope of 3.
  24. Graph of x = -2 which is a line of undefined slope that goes through the point (-2,0).
  25. [latex]y=3[/latex]
  26. [latex]x=-3[/latex]

Fitting Linear Models to Data

  1. [latex]2,300[/latex]
  3. [latex]64,170[/latex]
  5. [latex]P(t)=75,000+2500t[/latex]
  7. [latex](-30,0)[/latex] Thirty years before the start of this model, the town had no citizens. $$(0,75,000)$$ Initially, the town had a population of [latex]75,000[/latex].
  9. Ten years after the model began
  11. [latex]y=-2t+180[/latex]
  13. In 2070, the company’s profit will be zero.
  15. [latex]y=30t-300[/latex]
  17. [latex](10,0)[/latex] In the year 1990, the company’s profits were zero
    1. [latex]696[/latex] people
    2. [latex]4[/latex] years
    3. [latex]174[/latex] people per year
    4. [latex]305[/latex] people
    5. [latex]P(t)=305+174t[/latex]
    6. [latex]2,219[/latex] people
    1. [latex]C(x)=0.15x+10[/latex]
    2. The flat monthly fee is [latex]$10[/latex] and there is a [latex]$0.15[/latex] fee for each additional minute used
    3. [latex]$113.05[/latex]
  21. [latex]P(t)=190t+4,360[/latex]
    1. [latex]R(t)=-2.1t+16[/latex]
    2. [latex]5.5[/latex] billion cubic feet
    3. During the year 2017
  23. No
    Scatterplot with a collection of points at (1,1); (3,9); (5,28); (7,65); (9,125); and (11,216); they do not appear linear
  24. No
    Scatterplot with a collection of points at (16,46); (18,50); (20,54); (25,55); and (30,62); they appear nonlinear
  25. Interpolation. About [latex]60°F[/latex].
  26. This value of [latex]r[/latex] indicates a strong positive correlation or slope, so D
  27. This value of [latex]r[/latex] indicates a strong negative correlation or slope, so C
  28. This value of [latex]r[/latex] indicates a weak negative correlation or slope, so B
  29. This value of [latex]r[/latex] indicates a weak negative correlation, so B
  30. Scatter plot with domain 0 to 10 and a range from -1 to 4 with the line of best fit drawn going through the points: (0,1.5); (1.5, -0.1); (2.1,1.9); (3.4, 1.5); (4.5,2.5); (5.8,2.2); (6.8,3.8); (7.8,3.6); (8.8,2); and (10,2.4).
  31. Scatter plot with a domain of 0 to 10 and a range of 2 to 6 and the line of best fit going through the points: (0,2.1); (1,3.9); (2.1,3.6); (3.6,3.9); (4.4,4); (5.6,4.2); (6.8,5); (7.8,5); (9,5.6); and (10,6)
  32. Yes, trend appears linear because [latex]r=0.985[/latex] and will exceed [latex]12,000[/latex] near midyear, [latex]2016[/latex], [latex]24.6[/latex] years since [latex]1992[/latex].
  33. [latex]y=1.640x+13,800[/latex], [latex]r=0.987[/latex]
  34. [latex]y=-0.962x+26.86[/latex], [latex]r=-0.965[/latex]
  35. [latex]y=-1.981x+60.197[/latex], [latex]r=-0.998[/latex]
  36. [latex]y=0.00587x+1985.41[/latex]
  37. 2032
  38. [latex]y=20.25x-671.5[/latex]
  39. approx [latex]82[/latex] units sold in hundreds
  40. [latex]y=-10.75x+742.50[/latex]
  41. approx [latex]67[/latex] units sold in hundreds