Question

Indicate in standard form the equation of the line through the given points. P(0, -4), Q(5.1)

Answer 1

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf P(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Q(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}}\implies \cfrac{1+4}{5}\implies \cfrac{5}{5}\implies 1$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{1}(x-\stackrel{x_1}{0})\implies y+4=x \\\\\\ y=x-4\implies -x+y=-4\implies x-y=4$