Question

Determine an equation of a line that passes through point P(3,-3)that is parallel to line m y=7/6x+5

Answer 1

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

`y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{6}}x+5\qquad \impliedby \qquad \begin{array} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`

so we are really looking at the equation of a line whose slope is 7/6 and it passes through (3 , -3)

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{6} \\\\\\ \begin{array}c \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}{(-3)}=\stackrel{m}{\cfrac{7}{6}}(x-\stackrel{x_1}{3}) \implies y +3 = \cfrac{7}{6} ( x -3) \\\\\\ y+3=\cfrac{7}{6}x-\cfrac{7}{2}\implies y=\cfrac{7}{6}x-\cfrac{7}{2}-3\implies {\Large \begin{array}{llll} y=\cfrac{7}{6}x-\cfrac{13}{2} \end{array}}`