# Solutions 8: Linear Functions

## Solutions to Try Its

1.
$m=\frac{4 - 3}{0 - 2}=\frac{1}{-2}=-\frac{1}{2}$
; decreasing because
$m<0$
.

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

3.
$y - 2=-2\left(x+2\right)$
;
$y=-2x - 2$

4.
$y - 0=-3\left(x - 0\right)$
;
$y=-3x$

5.
$y=-7x+3$

6.
$H\left(x\right)=0.5x+12.5$

## 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.
$d\left(t\right)=100 - 10t$

7. Yes.

9. No.

11. No.

13. No.

15. Increasing.

17. Decreasing.

19. Decreasing.

21. Increasing.

23. Decreasing.

25. 3

27.
$-\frac{1}{3}$

29.
$\frac{4}{5}$

31.
$f\left(x\right)=-\frac{1}{2}x+\frac{7}{2}$

33.
$y=2x+3$

35.
$y=-\frac{1}{3}x+\frac{22}{3}$

37.
$y=\frac{4}{5}x+4$

39.
$-\frac{5}{4}$

41.
$y=\frac{2}{3}x+1$

43.
$y=-2x+3$

45.
$y=3$

47. Linear,
$g\left(x\right)=-3x+5$

49. Linear,
$f\left(x\right)=5x - 5$

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

53. Linear,
$f\left(x\right)=10x - 24$

55.
$f\left(x\right)=-58x+17.3$

57.

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

61.

63.
$x=-\frac{16}{3}$

65.
$x=a$

67.
$y=\frac{d}{c-a}x-\frac{ad}{c-a}$

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