Question

Write the standard form of the equation of the line through the given point with the given slope.

through: (0,0), slope: 1/3



please help me, my math teacher can't teach

Answer 1

bearing 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 (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies \cfrac{1}{3} \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{1}{3}(x-0) \\\\\\ y=\cfrac{1}{3}x\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3y=x\implies -x+3y=0}\implies \stackrel{\textit{standard form}}{x-3y=0}`