Solutions 9: Graphs of Linear Functions

Solutions to Try Its

1.

Graph of the line y = (3/4)x + 6, with the points (0,6), (4,3) and (8,0) labeled. 2. Possible answers include
(−3,7)\left(-3,7\right)
,
(−6,9)\left(-6,9\right)
, or
(−9,11)\left(-9,11\right)
.

3.

4. 
(16, 0)\left(16,\text{ 0}\right)


5. a. 
f(x)=2xf\left(x\right)=2x


b.
g(x)=−12xg\left(x\right)=-\frac{1}{2}x


6. 
y=−13x+6y=-\frac{1}{3}x+6


7.

a. 

(0,5)\left(0,5\right)

b.

(5, 0)\left(5,\text{ 0}\right)

c. Slope -1

d. Neither parallel nor perpendicular

e. Decreasing function

f. Given the identity function, perform a vertical flip (over the t-axis) and shift up 5 units.

Solutions to Odd-Numbered Exercises

1. The slopes are equal; y-intercepts are not equal.

3. The point of intersection is
(a,a)\left(a,a\right)
. This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a. The point of intersection will have these two characteristics.

5. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation
y=mx+by=mx+b
and solve for b. Then write the equation of the line in the form
y=mx+by=mx+b
by substituting in m and b.

7. neither parallel or perpendicular

9. perpendicular

11. parallel

13. 
(−2, 0)\left(-2\text{, }0\right)
;
(0, 4)\left(0\text{, 4}\right)


15. 
(15, 0)\left(\frac{1}{5}\text{, }0\right)
;
(0, 1)\left(0\text{, 1}\right)


17. 
(8, 0)\left(8\text{, }0\right)
;
(0, 28)\left(0\text{, }28\right)


19. 
Line 1:m=8 Line 2:m=−6Neither\text{Line 1}: m=8 \text{ Line 2}: m=-6 \text{Neither}


21. 
Line 1:m=−12 Line 2:m=2Perpendicular\text{Line 1}: m=-\frac{1}{2} \text{ Line 2}: m=2 \text{Perpendicular}


23. 
Line 1:m=−2 Line 2:m=−2Parallel\text{Line 1}: m=-2 \text{ Line 2}: m=-2 \text{Parallel}


25. 
g(x)=3x−3g\left(x\right)=3x - 3


27. 
p(t)=−13t+2p\left(t\right)=-\frac{1}{3}t+2


29. 
(−2,1)\left(-2,1\right)


31. 
(−175,53)\left(-\frac{17}{5},\frac{5}{3}\right)


33. F

35. C

37. A

39.

41.

43.

45.

47.

49.

51.

53.

55.

57.

59. 
g(x)=0.75x−5.5g\left(x\right)=0.75x - 5.5\text{}
0.75 
(0,−5.5)\left(0,-5.5\right)


61. 
y=3y=3


63. 
x=−3x=-3


65. no point of intersection

67. 
(2, 7)\left(\text{2},\text{ 7}\right)


69. 
(−10, −5)\left(-10,\text{ }-5\right)


71. 
y=100x−98y=100x - 98


73. 
x<1999201x>1999201x<\frac{1999}{201}x>\frac{1999}{201}


75. Less than 3000 texts

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