Question

Write an equation of the line in point-slope form that passes through the given points.

(4,-3/4) and (2,5/4)

Answer 1

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{-(3)/(4)})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{(5)/(4)}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{(5)/(4)}-\stackrel{y1}{\left( -(3)/(4) \right)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{~~ (5 )/(4 )+(3)/(4) ~~}{-2} \\\\\\ \cfrac{~~ ( 5+3)/( 4) ~~}{-2}\implies \cfrac{~~ (8 )/(4 ) ~~}{-2}\implies \cfrac{2}{-2}\implies -1\qquad \impliedby m`

`\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(-(3)/(4) \right)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4})\implies {\large \begin{array}{llll} y+\cfrac{3}{4}=-(x-4) \end{array}}`