[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ -4}})\quad
% (c,d)
&({{ 5}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-4)}{5-0}\implies \cfrac{1+4}{5}\implies 1[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-4)=1(x-0)\implies y+4=x\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}[/tex]
now, the so-called standard form, is moving the variables to the left-hand-side, sort them in descending order according to their exponents, and usually alphabetically some, so the "x" is left of the "y" and so on
-x+y=-4
