Question

Line in standard from that passes through (35,30) and (20,-3)

Answer 1

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

`(\stackrel{x_1}{35}~,~\stackrel{y_1}{30})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{-3}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{30}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{35}}} \implies \cfrac{ -33 }{ -15 } \implies \cfrac{11}{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-\stackrel{y_1}{30}=\stackrel{m}{ \cfrac{11}{5}}(x-\stackrel{x_1}{35}) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-30)=5\left(\cfrac{11}{5}(x-35) \right)}\implies 5y-150=11(x-35) \\\\\\ 5y-150=11x-385\implies 5y=11x-235 \\\\\\ -11x+5y=-235\implies 11x-5y=235\impliedby \textit{standard form}`