Question

HELP ME PLEASE!!!!!

Write an equation of the line with slope 2/5 through the point (-5,4). Give final answer in standard form

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}{-5}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{5} \\\\\\ \begin{array}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}{ \cfrac{2}{5}}(x-\stackrel{x_1}{(-5)})\implies y-4=\cfrac{2}{5}(x+5)`

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y-4)=5\left( \cfrac{2}{5}(x+5) \right)}\implies 5y-20=2(x+5)\implies 5y-20=2x+10 \\\\\\ -2x+5y-20=10\implies -2x+5y=30\implies 2x-5y=-30`