Question

A line passes through (10,4) and (13,-11). Write the equation of the line in standard form.

A.
5x - y = 46
B.
5x + y = 46
C.
5x + y = 54
D.
5x - y = 10

Answer 1

`\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{-11}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-11-4}{13-10}\implies \cfrac{-15}{3}\implies -5 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-5(x-10)`

now

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

therefore,

`\bf y-4=-5(x-10)\implies y-4=-5x+50\implies \blacktriangleright 5x+y=54 \blacktriangleleft`