Question

Indicate in standard form the equation of the line through the given points.

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ -4}})\quad % (c,d) &({{ 5}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-4)}{5-0}\implies \cfrac{1+4}{5}\implies 1$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-4)=1(x-0)\implies y+4=x\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}$

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