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Study Guides > MATH 1314: College Algebra

Solutions

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. (20)\left(-2\text{, }0\right)\\ ; (0, 4)\left(0\text{, 4}\right)\\ 15. (150)\left(\frac{1}{5}\text{, }0\right)\\ ; (0, 1)\left(0\text{, 1}\right)\\ 17. (80)\left(8\text{, }0\right)\\ ; (028)\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)=3x3g\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)=0.75x5.5g\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=100x98y=100x - 98\\ 73. x<1999201x>1999201x<\frac{1999}{201}x>\frac{1999}{201}\\ 75. Less than 3000 texts  

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