Chapter 5
Section 5.1: Equations of Lines
1. 5 3. $-5$ 5. $-{\scriptstyle{}^{9}\!\!\diagup\!\!{}_{10}\;}$ 7. 0 9. The slope is undefined
11. $y=-\tfrac{3}{4}x+3$ $m=-\tfrac{3}{4}$ $y\text{-intercept}=3$ 13. $y=-\tfrac{1}{5}x+\tfrac{3}{5}$ $m=-\tfrac{1}{5}$ $y\text{-intercept}=\tfrac{3}{5}$ 15. $y=\tfrac{4}{3}x-2$ $m=\tfrac{4}{3}$ $y\text{-intercept}=-2$ 17. $y=4x-11$ $m=4$ $y\text{-intercept}=-11$
19. $y=-\tfrac{3}{2}x+5$ $m=-\tfrac{3}{2}$ $y\text{-intercept}=5$ 21. $(0,3),\text{ }(4,0)$ 23. $(3,6),\text{ }(4,8)$ 25. $(-1,5),\text{ }(2,0)$
27. $(-1,-3),\,(0,-4)$ 29. $(0,5),\text{ }(1,6)$ 31. $-2x+3y=15$
33. $3x+2y=-12$ 35. $3x-5y=12$
37. $5x+2y=-2$ 39. $3x+2y=7$
Section 5.2: Graphs of Lines
1. $y-3=\tfrac{2}{5}(x-2)$ |
3. $y+3=-\tfrac{1}{3}(x-4)$ |
5. $y=-3$ |
7. $y-4=\frac{1}{6}(x-4)$ |
$y=x-8$
11. $y=\tfrac{2}{3}x+1$
13. $y=-\tfrac{3}{2}\left( x-1 \right)$
15. $y-3=\tfrac{1}{4}\left( x-2 \right)$
17. a. F b. C c. G d. B e. A f. H
19. The slope is negative. The slope is positive.
Section 5.3: Parallel and Perpendicular Lines
1. $y=3x+5$ 3. $y=\tfrac{1}{2}x+1$ 5. $y=\tfrac{4}{7}x$
7. $y-3=-\tfrac{3}{2}(x+1)$ 9. $y=-\tfrac{1}{5}x+4$ 11. $x=2$
13. $y+3=-\tfrac{9}{4}(x+1)$ 15. $y=-\tfrac{3}{2}x+3$ 17. $y+3=\tfrac{3}{2}(x+1)$
19. $y-4=-\tfrac{3}{5}(x+11)$ 21. $x=-1$ 23. Parallel; both have slope $m=\tfrac{4}{3}$
25. a. $y-3=\tfrac{2}{3}(x-2)$ b. $y-3=-\tfrac{3}{2}(x-2)$ c. $y-2=\tfrac{2}{3}(x+4)$ d. $y-2=-\tfrac{3}{2}(x+4)$
Section 5.4: Intersection of Lines by Substitution
1. $\left( 3,-1 \right)$ 3. $\left( {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;},1 \right)$ 5. $\left( 6,2 \right)$ 7. $\left( 3,4 \right)$ 9. $\left( 3,-5 \right)$
11. $\left( 1,{\scriptstyle{}^{3}\!\!\diagup\!\!{}_{2}\;} \right)$ 13. $\left( -1,2 \right)$ 15. $\left( 9,6 \right)$ 17. $\left( -{\scriptstyle{}^{12}\!\!\diagup\!\!{}_{13}\;},-{\scriptstyle{}^{47}\!\!\diagup\!\!{}_{13}\;} \right)$
19. $\left( -1,{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;} \right)$ 21. $\left( 3,12 \right)$ 23. $\left( 25,6 \right)$ 25. $\left( 3,5 \right)$ 27. $\left( 2,3 \right)$
Section 5.5: Intersection of Lines by Elimination
1. $\left( -1,2 \right)$ 3. $\left( 2,-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;} \right)$ 5. $\left( 2,-3 \right)$ 7. $\left( 7,-2 \right)$ 9. $\left( {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{3}\;},{\scriptstyle{}^{2}\!\!\diagup\!\!{}_{3}\;} \right)$
11. $\left( {\scriptstyle{}^{7}\!\!\diagup\!\!{}_{2}\;},{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;} \right)$ 13. $\left( 4,1 \right)$ 15. $\left( -4,-7 \right)$ 17. $\left( {\scriptstyle{}^{9}\!\!\diagup\!\!{}_{4}\;},{\scriptstyle{}^{13}\!\!\diagup\!\!{}_{8}\;} \right)$ 19. $\left( 3,1 \right)$
21. $\left( 2,-1 \right)$ 23. $\left( 16,-{\scriptstyle{}^{21}\!\!\diagup\!\!{}_{2}\;} \right)$ 25. $\left( -{\scriptstyle{}^{25}\!\!\diagup\!\!{}_{22}\;},{\scriptstyle{}^{51}\!\!\diagup\!\!{}_{22}\;} \right)$ 27. $\left( {\scriptstyle{}^{53}\!\!\diagup\!\!{}_{37}\;},-{\scriptstyle{}^{51}\!\!\diagup\!\!{}_{37}\;} \right)$
Section 5.6: Intersection of Lines by Graphing
1. 3. 5.
7. 9. 11.
13. $\left( 5,3 \right)$ 15. $\left( {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;},{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{3}\;} \right)$ 17. $\left( {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;},-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;} \right)$ 19. $\left( {\scriptstyle{}^{1}\!\!\diagup\!\!{}_{3}\;},-{\scriptstyle{}^{1}\!\!\diagup\!\!{}_{2}\;} \right)$