Question

What is the equation of the line that passes through the point left bracket, 6, comma, 1, right bracket(6,1) and has a slope of minus, one half

Answer 1

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{1}{2} \\\\\\ \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}{1}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{6}) \\\\\\ y-1=-\cfrac{1}{2}x+3\implies {\Large \begin{array}{llll} y=-\cfrac{1}{2}x+4 \end{array}}`