Answer Key 3.6
- \(m=2\)
- \(m=-\dfrac{2}{3}\)
- \(m=4\)
- \(m=-10\)
- \(\begin{array}{rrrrlrrr}
\\ \\ \\ \\
x&-&y&=&4&&& \\
-x&&&&-x&&& \\
\hline
&&(-y&=&-x&+&4)&(-1) \\
&&y&=&x&-&4& \\
&&m&=&1&&&
\end{array}\) - \(\begin{array}{rrrrlrrr}
\\ \\ \\ \\ \\ \\ \\ \\
6x&-&5y&=&20&&& \\
-6x&&&&-6x&&& \\
\hline
&&\dfrac{-5y}{-5}&=&\dfrac{-6x}{-5}&+&\dfrac{20}{-5}& \\ \\
&&y&=&\dfrac{6}{5}x&-&4& \\ \\
&&m&=&\dfrac{6}{5}&&&
\end{array}\) - \(\begin{array}{rrlrrr}
\\ \\ \\ \\ \\
y&=&\dfrac{1}{3}x&&& \\ \\
\therefore m&=&\dfrac{1}{3} &&& \\
m_{\perp} &=&-1&\div &\dfrac{1}{3}&\text{or} \\
m_{\perp}&=&-3 &&&
\end{array}\) - \(\begin{array}{lrlrrrr}
\\ \\ \\ \\
m&=&-\dfrac{1}{2} &&&& \\
m_{\perp} &=&-1&\div &-\dfrac{1}{2}&&\\ \\
m_{\perp}&=&-1 &\cdot &-\dfrac{2}{1}&=& 2
\end{array}\) - \(\begin{array}{lrlrrrr}
\\ \\ \\ \\
m&=&-\dfrac{1}{3} &&&& \\
m_{\perp} &=&-1&\div &-\dfrac{1}{3}&&\\ \\
m_{\perp}&=&-1 &\cdot &-\dfrac{3}{1}&=& 3
\end{array}\) - \(\begin{array}{lrlrrrr}
\\ \\ \\ \\
m&=&\dfrac{4}{5} &&&& \\
m_{\perp} &=&-1&\div &\dfrac{4}{5}&&\\ \\
m_{\perp}&=&-1 &\cdot &\dfrac{5}{4}&=& -\dfrac{5}{4}
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\
x&-&3y&=&-6& \\
-x&&&&-x&& \\
\hline
&&\dfrac{-3y}{-3}&=&\dfrac{-x}{-3}&-&\dfrac{6}{-3} \\ \\
&&y&=&\dfrac{1}{3}x&+&2 \\
&&m_{\perp}&=&-1&\div &\dfrac{1}{3} \\
&&m_{\perp}&=&-3&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\
3x&-&y&=&-3& \\
-3x&&&&-3x&& \\
\hline
&&-y&=&-3x&-&3 \\
&&y&=&3x&+&3 \\
&&m_{\perp}&=&-1&\div &3 \\
&&m_{\perp}&=&-\dfrac{1}{3}&&
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
m&=&\dfrac{2}{5}&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&4&=&\dfrac{2}{5}(x&-&1) \\ \\
y&-&4&=&\dfrac{2}{5}x&-&\dfrac{2}{5} \\ \\
&+&4&&&+&4 \\
\hline
&&y&=&\dfrac{2}{5}x&+&\dfrac{18}{5}
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\
m&=&-3&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&2&=&-3(x&-&5) \\
y&-&2&=&-3x&+&15 \\
&+&2&&&+&2 \\
\hline
&&y&=&-3x&+&17
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
m&=&\dfrac{1}{2}&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&4&=&\dfrac{1}{2}(x&-&3) \\ \\
y&-&4&=&\dfrac{1}{2}x&-&\dfrac{3}{2} \\ \\
&+&4&&&+&4 \\
\hline
&&y&=&\dfrac{1}{2}x&+&\dfrac{5}{2}
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
m&=&\dfrac{4}{3}&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&-1&=&\dfrac{4}{3}(x&-&1) \\ \\
y&+&1&=&\dfrac{4}{3}x&-&\dfrac{4}{3} \\ \\
&-&1&&&-&1 \\
\hline
&&y&=&\dfrac{4}{3}x&-&\dfrac{7}{3}
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
m&=&-\dfrac{3}{5}&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&3&=&-\dfrac{3}{5}(x&-&2) \\ \\
y&-&3&=&-\dfrac{3}{5}x&+&\dfrac{6}{5} \\ \\
&+&3&&&+&3 \\
\hline
&&y&=&-\dfrac{3}{5}x&+&\dfrac{21}{5}
\end{array}\) - \(\begin{array}{rrrrlrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
m&=&\dfrac{1}{3}&&&& \\ \\
y&-&y_1&=&m(x&-&x_1) \\
y&-&3&=&\dfrac{1}{3}(x&-&-1) \\ \\
y&-&3&=&\dfrac{1}{3}x&+&\dfrac{1}{3} \\ \\
&+&3&&&+&3 \\
\hline
&&y&=&\dfrac{1}{3}x&+&\dfrac{10}{3}
\end{array}\) - \(\begin{array}{rrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-x&+&y&=&1&&&& \\
+x&&&&+x&&&& \\
\hline
&&y&=&x&+&1&& \\
&&\therefore m&=&1&&&& \\ \\
y&-&y_1&=&m(x&-&x_1)&& \\
y&-&-5&=&1(x&-&1)&& \\
y&+&5&=&x&-&1&& \\
-y&-&5&&-y&-&5&& \\
\hline
&&0&=&x&-&y&-&6
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-x&+&2y&=&2&&& \\
+x&&&&+x&&& \\
\hline
&&2y&=&x&+&2& \\
&\text{or}&y&=&\dfrac{1}{2}x&+&1& \\ \\
&&\therefore m&=&-2&&& \\ \\
y&-&y_1&=&m(x&-&x_1)& \\
y&-&-2&=&-2(x&-&1)& \\
y&+&2&=&-2x&+&2& \\
-y&-&2&&-y&-&2& \\
\hline
&&(0&=&-2x&-&y)&(-1) \\
&&0&=&2x&+&y&
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
5x&+&y&=&-3&&&&& \\
-5x&&&&-5x&&&&& \\
\hline
&&y&=&-5x&-&3&&& \\
&&\therefore m&=&-5&&&&& \\ \\
y&-&y_1&=&m(x&-&x_1)&&& \\
y&-&2&=&-5(x&-&5)&&& \\
y&-&2&=&-5x&+&25&&& \\
-y&+&2&&-y&+&2&&& \\
\hline
&&(0&=&-5x&-&y&+&27)&(-1) \\
&&0&=&5x&+&y&-&27&
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-x&+&y&=&1&&&&& \\
+x&&&&+x&&&&& \\
\hline
&&y&=&x&+&1&&& \\
&&\therefore m&=&-1&&&&& \\ \\
y&-&y_1&=&m(x&-&x_1)&&& \\
y&-&3&=&-1(x&-&1)&&& \\
y&-&3&=&-x&+&1&&& \\
-y&+&3&&-y&+&3&&& \\
\hline
&&(0&=&-x&-&y&+&4)&(-1) \\
&&0&=&x&+&y&-&4&
\end{array}\) - \(\begin{array}{rrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-4x&+&y&=&0&&&& \\
+4x&&&&+4x&&&& \\
\hline
&&y&=&4x&&&& \\
&&\therefore m&=&4&&&& \\ \\
y&-&y_1&=&m(x&-&x_1)&& \\
y&-&2&=&4(x&-&4)&& \\
y&-&2&=&4x&-&16&& \\
-y&+&2&&-y&+&2&& \\
\hline
&&0&=&4x&-&y&-&14
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
3x&+&7y&=&0&&&&& \\
-3x&&&&-3x&&&&& \\
\hline
&&7y&=&-3x&&&&& \\
&\text{or}&y&=&-\dfrac{3}{7}x&&&&& \\ \\
&&\therefore m&=&\dfrac{7}{3}&&&&& \\ \\
y&-&y_1&=&m(x&-&x_1)&&& \\
y&-&-5&=&\dfrac{7}{3}(x&-&-3)&&& \\ \\
y&+&5&=&\dfrac{7}{3}x&+&7&&& \\ \\
-y&-&5&&-y&-&5&&& \\
\hline
&&(0&=&\dfrac{7}{3}x&-&y&+&2)&(3) \\ \\
&&0&=&7x&-&3y&+&6&
\end{array}\) - \(y=-3\)
- \(x=-5\)
- \(x=-3\)
- \(y=0\)
- \(y=-1\)
- \(x=2\)
- \(x=-2\)
- \(y=-4\)
- \(y=3\)
- \(x=-3\)
- \(x=5\)
- \(y=-1\)
