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 [latex]\left(-3,7\right)[/latex], [latex]\left(-6,9\right)[/latex], or [latex]\left(-9,11\right)[/latex].

3.

4. [latex]\left(16,\text{ 0}\right)[/latex]

5. a. [latex]f\left(x\right)=2x[/latex]
b. [latex]g\left(x\right)=-\frac{1}{2}x[/latex]

6. [latex]y=-\frac{1}{3}x+6[/latex]

7.

a. [latex]\left(0,5\right)[/latex]

b. [latex]\left(5,\text{ 0}\right)[/latex]

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 [latex]\left(a,a\right)[/latex]. 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 [latex]y=mx+b[/latex] and solve for b. Then write the equation of the line in the form [latex]y=mx+b[/latex] by substituting in m and b.

7. neither parallel or perpendicular

9. perpendicular

11. parallel

13. [latex]\left(-2\text{, }0\right)[/latex] ; [latex]\left(0\text{, 4}\right)[/latex]

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

17. [latex]\left(8\text{, }0\right)[/latex] ; [latex]\left(0\text{, }28\right)[/latex]

19. [latex]\text{Line 1}: m=8 \text{ Line 2}: m=-6 \text{Neither}[/latex]

21. [latex]\text{Line 1}: m=-\frac{1}{2} \text{ Line 2}: m=2 \text{Perpendicular}[/latex]

23. [latex]\text{Line 1}: m=-2 \text{ Line 2}: m=-2 \text{Parallel}[/latex]

25. [latex]g\left(x\right)=3x - 3[/latex]

27. [latex]p\left(t\right)=-\frac{1}{3}t+2[/latex]

29. [latex]\left(-2,1\right)[/latex]

31. [latex]\left(-\frac{17}{5},\frac{5}{3}\right)[/latex]

33. F

35. C

37. A

39.

41.

43.

45.

47.

49.

51.

53.

55.

57.

59. [latex]g\left(x\right)=0.75x - 5.5\text{}[/latex] 0.75 [latex]\left(0,-5.5\right)[/latex]

61. [latex]y=3[/latex]

63. [latex]x=-3[/latex]

65. no point of intersection

67. [latex]\left(\text{2},\text{ 7}\right)[/latex]

69. [latex]\left(-10,\text{ }-5\right)[/latex]

71. [latex]y=100x - 98[/latex]

73. [latex]x<\frac{1999}{201}x>\frac{1999}{201}[/latex]

75. Less than 3000 texts