Solutions 8: Linear Functions

Solutions to Try Its

1. 
m=4302=12=12m=\frac{4 - 3}{0 - 2}=\frac{1}{-2}=-\frac{1}{2}
; decreasing because
m<0m<0
.

2. 
m=1,8681,4422,0122,009=4263=142 people per yearm=\frac{1,868 - 1,442}{2,012 - 2,009}=\frac{426}{3}=142\text{ people per year}


3. 
y2=2(x+2)y - 2=-2\left(x+2\right)
;
y=2x2y=-2x - 2


4. 
y0=3(x0)y - 0=-3\left(x - 0\right)
;
y=3xy=-3x


5. 
y=7x+3y=-7x+3


6. 
H(x)=0.5x+12.5H\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(t)=10010td\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. 
13-\frac{1}{3}


29. 
45\frac{4}{5}


31. 
f(x)=12x+72f\left(x\right)=-\frac{1}{2}x+\frac{7}{2}


33. 
y=2x+3y=2x+3


35. 
y=13x+223y=-\frac{1}{3}x+\frac{22}{3}


37. 
y=45x+4y=\frac{4}{5}x+4


39. 
54-\frac{5}{4}


41. 
y=23x+1y=\frac{2}{3}x+1


43. 
y=2x+3y=-2x+3


45. 
y=3y=3


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


49. Linear,
f(x)=5x5f\left(x\right)=5x - 5


51. Linear,
g(x)=252x+6g\left(x\right)=-\frac{25}{2}x+6


53. Linear,
f(x)=10x24f\left(x\right)=10x - 24


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


57.

59. a.
a=11,900a=11,900
;
b=1001.1b=1001.1
b.
q(p)=1000p100q\left(p\right)=1000p - 100


61.

.. 63. 
x=163x=-\frac{16}{3}


65. 
x=ax=a


67. 
y=dcaxadcay=\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

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