Answer Key 3.4

For questions 1 to 10, sketch the linear equation using the slope intercept method.

1. [latex]y = -\dfrac{1}{4}x - 3[/latex]
2. [latex]y = \dfrac{3}{2}x - 1[/latex]     
3. [latex]y = -\dfrac{5}{4}x - 4[/latex]       
4. [latex]y = -\dfrac{3}{5}x + 1[/latex]    
5. [latex]y = -\dfrac{4}{3}x + 2[/latex]       
6. [latex]y = \dfrac{5}{3}x + 4[/latex]     
7. [latex]y = \dfrac{3}{2}x - 5[/latex]    
8. [latex]y = -\dfrac{2}{3}x - 2[/latex]     
9. [latex]y = -\dfrac{4}{5}x - 3[/latex]     
10. [latex]y = \dfrac{1}{2}x[/latex]     

For questions 11 to 20, sketch the linear equation using the [latex]x[/latex] and [latex]y[/latex] intercepts.

11. [latex]x + 4y = -4[/latex]    
12. [latex]2x - y = 2[/latex]     
13. [latex]2x + y = 4[/latex]     
14. [latex]3x + 4y = 12[/latex]   
15. [latex]2x - y = 2[/latex]   
16. [latex]4x + 3y = -12[/latex]    
17. [latex]x + y = -5[/latex]   
18. [latex]3x + 2y = 6[/latex]   
19. [latex]x - y = -2[/latex]   
20. [latex]4x - y = -4[/latex]   

For questions 21 to 28, sketch the linear equation using any method.

21. [latex]y = -\dfrac{1}{2}x + 3[/latex]   
22. [latex]y = 2x - 1[/latex]    
23. [latex]y = -\dfrac{5}{4}x[/latex]    
24. [latex]y = -3x + 2[/latex]    
25. [latex]y = -\dfrac{3}{2}x + 1[/latex]    
26. [latex]y = \dfrac{1}{3}x - 3[/latex]     
27. [latex]y = \dfrac{3}{2}x + 2[/latex]     
28. [latex]y = 2x - 2[/latex]     

29. [latex]\begin{array}{rrrrrrr} y& +& 3& =& -\dfrac{4}{5}x& +& 3 \\ &-&3&&&-&3 \\ \hline &&y&=&-\dfrac{4}{5}x&& \end{array}[/latex]
30. [latex]\begin{array}{rrrrrrr} y&-&4&=&\dfrac{1}{2}x&& \\ &+&4&&&+&4 \\ \hline &&y&=&\dfrac{1}{2}x&+&4 \end{array}[/latex]    
31. [latex]\begin{array}{rrrrrrr} x& +& 5y& =& -3& +& 2y \\ -x&-&2y&&-x&-&2y \\ \hline &&3y&=&-x&-&3 \\ &&y&=&-\dfrac{1}{3}x&-&1 \end{array}[/latex]   
32. [latex]\begin{array}{rrrrrrrrr} 3x& -& y& =& 4& +& x& -& 2y \\ -3x&+&2y&&&-&3x&+&2y \\ \hline &&y&=&-2x&+&4&& \end{array}[/latex]   
33. [latex]\begin{array}{rrrrrrrr} 4x&+&3y&=&5(x&+&y)& \\ 4x&+&3y&=&5x&+&5y& \\ -4x&-&5y&&-4x&-&5y& \\ \hline &&\dfrac{-2y}{-2}&=&\dfrac{x}{-2}&&& \\ \\ &&y&=&-\dfrac{1}{2}x&&& \end{array}[/latex]    
34. [latex]\begin{array}{rrrrrrr} 3x&+&4y&=&12&-&2y \\ -3x&+&2y&&-3x&+&2y \\ \hline &&\dfrac{6y}{6}&=&\dfrac{-3x}{6}&+&\dfrac{12}{6} \\ \\ &&y&=&-\dfrac{1}{2}x&+&2 \end{array}[/latex]    
35. [latex]\begin{array}{rrrrrrr} 2x&-&y&=&2&-&y \\ &+&y&&&+&y \\ \hline &&2x&=&2&& \\ &&x&=&1&& \end{array}[/latex]    
36. [latex]\begin{array}{rrrrrrrrr} 7x&+&3y&=&2(2x&+&2y)&+&6 \\ 7x&+&3y&=&4x&+&4y&+&6 \\ -7x&-&4y&&-7x&-&4y&& \\ \hline &&-y&=&-3x&+&6&& \\ &&y&=&3x&-&6&& \end{array}[/latex]    
37. [latex]\begin{array}{rrrrrrr} x&+&y&=&-2x&+&3 \\ -x&&&&-\phantom{1}x&& \\ \hline &&y&=&-3x&+&3 \end{array}[/latex]    
38. [latex]\begin{array}{rrrrrrr} 3x&+&4y&=&3y&+&6 \\ -3x&-&3y&&-3y&-&3x \\ \hline &&y&=&-3x&+&6 \end{array}[/latex]    
39. [latex]\begin{array}{rrrrrrrrr} 2(x&+&y)&=&-3(x&+&y)&+&5 \\ 2x&+&2y&=&-3x&-&3y&+&5 \\ -2x&+&3y&&-2x&+&3y&& \\ \hline &&5y&=&-5x&+&5&& \\ &&y&=&-x&+&1&& \end{array}[/latex]    
40. [latex]\begin{array}{rrrrrrr} 9x&-&y&=&4x&+&5 \\ -9x&&&&-9x&& \\ \hline &&-y&=&-5x&+&5 \\ &&y&=&5x&-&5 \end{array}[/latex]