Question

What is and equation of the line with slope 3 that goes through point (-½, 5/2)?

Answer 1

`\bf (\stackrel{x_1}{-(1)/(2)}~,~\stackrel{y_1}{(5)/(2)})~\hspace{10em} 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-\cfrac{5}{2}=3\left[ x-\left(-\cfrac{1}{2} \right) \right]\implies y-\cfrac{5}{2}=3\left( x+\cfrac{1}{2} \right) \\\\\\ y-\cfrac{5}{2}=3x+\cfrac{3}{2}\implies y==3x+\cfrac{3}{2}+\cfrac{5}{2}\implies y=3x+\cfrac{8}{2}\implies y=3x+4`