namely, what's the equation of a line that passes through (1,-1) and (5,5)
well, first off let's find its slope, and the plug all those values in the point-slope form.
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ -1}})\quad
% (c,d)
&({{ 5}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-(-1)}{5-1}\implies \cfrac{5+1}{5-1}
\\\\\\
\cfrac{6}{4}\implies \cfrac{3}{2}[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=\cfrac{3}{2}(x-1)
\\\\\\
y+1=\cfrac{3}{2}x-\cfrac{3}{2}\implies y=\cfrac{3}{2}x-\cfrac{3}{2}-1\implies y=\cfrac{3}{2}x-\cfrac{5}{2}[/tex]
