Question

Which equation represents a line that
passes through (2, -1/2)and has a slope of 3?

Answer 1

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-(1)/(2)}) \hspace{5em} \stackrel{slope}{m}\implies 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}{\left( -\cfrac{1}{2} \right)}=\stackrel{m}{3}(x-\stackrel{x_1}{2}) \implies y+\cfrac{1}{2}=3(x-2) \\\\\\ y+\cfrac{1}{2}=3x-6\implies y=3x-6-\cfrac{1}{2}\implies {\Large \begin{array}{llll} y=3x-\cfrac{13}{2} \end{array}}`