[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 1}})\quad
% (c,d)
&({{ 7}}\quad ,&{{ 4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-1}{7-1}\implies \cfrac{3}{6}\implies \cfrac{1}{2}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=\cfrac{1}{2}(x-1)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-1=\cfrac{1}{2}x-\cfrac{1}{2}\implies y=\cfrac{1}{2}x-\cfrac{1}{2}+1\implies y=\cfrac{1}{2}x+\cfrac{1}{2}[/tex]
