Question

1.

Write the equation of the line passing through the points in the given table
(-6,0) (-3,-1.5) (0,-3)

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use hmmm (-6 , 0) and (0 , -3)

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{ -3 }{0 +6} \implies \cfrac{ -3 }{ 6 } \implies -\cfrac{1}{2}`

`\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}{0}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = -\cfrac{1}{2} ( x +6) \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-\cfrac{1}{2}x-3 \end{array}} ~\hfill~`