Solutions 8: Linear Functions

Solutions to Try Its

1. [latex]m=\frac{4 - 3}{0 - 2}=\frac{1}{-2}=-\frac{1}{2}[/latex] ; decreasing because [latex]m<0[/latex].

2. [latex]m=\frac{1,868 - 1,442}{2,012 - 2,009}=\frac{426}{3}=142\text{ people per year}[/latex]

3. [latex]y - 2=-2\left(x+2\right)[/latex]; [latex]y=-2x - 2[/latex]

4. [latex]y - 0=-3\left(x - 0\right)[/latex] ; [latex]y=-3x[/latex]

5. [latex]y=-7x+3[/latex]

6. [latex]H\left(x\right)=0.5x+12.5[/latex]

Solutions to Odd-Numbered Exercises

1. Terry starts at an elevation of 3000 feet and descends 70 feet per second.

3. 3 miles per hour

5. [latex]d\left(t\right)=100 - 10t[/latex]

7. Yes.

9. No.

11. No.

13. No.

15. Increasing.

17. Decreasing.

19. Decreasing.

21. Increasing.

23. Decreasing.

25. 3

27. [latex]-\frac{1}{3}[/latex]

29. [latex]\frac{4}{5}[/latex]

31. [latex]f\left(x\right)=-\frac{1}{2}x+\frac{7}{2}[/latex]

33. [latex]y=2x+3[/latex]

35. [latex]y=-\frac{1}{3}x+\frac{22}{3}[/latex]

37. [latex]y=\frac{4}{5}x+4[/latex]

39. [latex]-\frac{5}{4}[/latex]

41. [latex]y=\frac{2}{3}x+1[/latex]

43. [latex]y=-2x+3[/latex]

45. [latex]y=3[/latex]

47. Linear, [latex]g\left(x\right)=-3x+5[/latex]

49. Linear, [latex]f\left(x\right)=5x - 5[/latex]

51. Linear, [latex]g\left(x\right)=-\frac{25}{2}x+6[/latex]

53. Linear, [latex]f\left(x\right)=10x - 24[/latex]

55. [latex]f\left(x\right)=-58x+17.3[/latex]

57.

59. a. [latex]a=11,900[/latex] ; [latex]b=1001.1[/latex] b. [latex]q\left(p\right)=1000p - 100[/latex]

61.
..

63. [latex]x=-\frac{16}{3}[/latex]

65. [latex]x=a[/latex]

67. [latex]y=\frac{d}{c-a}x-\frac{ad}{c-a}[/latex]

69. $45 per training session.

71. The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.

73. The slope is –400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.

75. c