Question

Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?

y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
y = one-third x + 1
can somone tell me which is right?

Answer 1

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \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-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -1 = \cfrac{1}{3} ( x +2) \\\\\\ y-1=\cfrac{1}{3}x+\cfrac{2}{3}\implies y=\cfrac{1}{3}x+\cfrac{2}{3}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{5}{3} \end{array}}`