5)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 5}}\quad ,&{{ -3}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -1
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-3)=-1(x-5)
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y+3=-x+5\implies y=-x+2[/tex]
6)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 2}}\quad ,&{{ 1}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 3
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=3(x-2)
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-1=3x-6\implies y=3x-5[/tex]
7)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 5}}\quad ,&{{ 2}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 0
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=0(x-5)
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-2=0\implies y=2[/tex]
8)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -2}}\quad ,&{{ 0}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2))
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]
9)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -2}}\quad ,&{{ 0}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2))
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]
10)
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{-2}}\quad ,&{{ -2}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-2)=\cfrac{3}{2}(x-(-2))
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y+2=\cfrac{3}{2}(x+2)\implies y+2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+1[/tex]
