Solutions

Solutions to Try Its

1. [latex]x=-5[/latex]

2. [latex]x=-3[/latex]

3. [latex]x=\frac{10}{3}[/latex]

4. [latex]x=1[/latex]

5. [latex]x=-\frac{7}{17}[/latex]. Excluded values are [latex]x=-\frac{1}{2}[/latex] and [latex]x=-\frac{1}{3}[/latex].

6. [latex]x=\frac{1}{3}[/latex]

7. [latex]m=-\frac{2}{3}[/latex]

8. [latex]y=4x - 3[/latex]

9. [latex]x+3y=2[/latex]

10. Horizontal line: [latex]y=2[/latex]

11. Parallel lines: equations are written in slope-intercept form.
Coordinate plane with the x-axis ranging from negative 5 to 5 and the y-axis ranging from negative 1 to 6. Two functions are graphed on the same plot: y = x/2 plus 5 and y = x/2 plus 2. The lines do not cross.

12. [latex]y=5x+3[/latex]

Solutions to Odd-Numbered Exercises

1. It means they have the same slope.

3. The exponent of the [latex]x[/latex] variable is 1. It is called a first-degree equation.

5. If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

7. [latex]x=2[/latex]

9. [latex]x=\frac{2}{7}[/latex]

11. [latex]x=6[/latex]

13. [latex]x=3[/latex]

15. [latex]x=-14[/latex]

17. [latex]x\ne -4[/latex]; [latex]x=-3[/latex]

19. [latex]x\ne 1[/latex]; when we solve this we get [latex]x=1[/latex], which is excluded, therefore NO solution

21. [latex]x\ne 0[/latex]; [latex]x=\frac{-5}{2}[/latex]

23. [latex]y=\frac{-4}{5}x+\frac{14}{5}[/latex]

25. [latex]y=\frac{-3}{4}x+2[/latex]

27. [latex]y=\frac{1}{2}x+\frac{5}{2}[/latex]

29. [latex]y=-3x - 5[/latex]

31. [latex]y=7[/latex]

33. [latex]y=-4[/latex]

35. [latex]8x+5y=7[/latex]

37. Parallel
Coordinate plane with the x and y axes ranging from negative 10 to 10. The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot. The lines do not cross.

39. Perpendicular
Coordinate plane with the x and y axes ranging from negative 10 to 10. The function y = negative 3 and the line x = 4 are graphed on the same plot. These lines cross at a 90 degree angle.

41. [latex]m=\frac{-9}{7}[/latex]

43. [latex]m=\frac{3}{2}[/latex]

45. [latex]{m}_{1}=\frac{-1}{3},\text{ }{m}_{2}=3;\text{ }\text{Perpendicular}[/latex]

47. [latex]y=0.245x - 45.662[/latex]. Answers may vary. [latex]{y}_{\text{min}}=-50,\text{ }{y}_{\text{max}}=-40[/latex]

49. [latex]y=-2.333x+6.667[/latex]. Answers may vary. [latex]{y}_{\mathrm{min}}=-10, {y}_{\mathrm{max}}=10[/latex]

51. [latex]y=\frac{-A}{B}x+\frac{C}{B}[/latex]

53. Yes, they are perpendicular.

[latex]\begin{array}{l}\text{The slope for }\left(-1,1\right)\text{ to }\left(0,4\right)\text{ is }3.\\ \text{The slope for }\left(-1,1\right)\text{ to }\left(2,0\right)\text{ is }\frac{-1}{3}.\\ \text{The slope for }\left(2,0\right)\text{ to }\left(3,3\right)\text{ is }3.\\ \text{The slope for }\left(0,4\right)\text{ to }\left(3,3\right)\text{ is }\frac{-1}{3}\end{array}[/latex].

55. 30 ft

57. $57.50

59. 220 mi