Question

2. A line passing through (6, a) and (9,-4) is parallel to y = 2/3x - 6. What is the value of a?

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{2}{3}}x -6 \impliedby \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 its slope is 2/3 hmmmm

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{a})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{a}}}{\underset{\textit{\large run}} {\underset{x_2}{9}-\underset{x_1}{6}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{2}{3}}\implies \cfrac{-4-a}{3}=\cfrac{2}{3}\implies -12-3a=6 \\\\\\ -12=6+3a\implies -18=3a\implies \cfrac{-18}{3}=a\implies -6=a`