Question

a graph of a linear equation passes through (-2,0) and (0,-6). Is 3x-y=-6 an equation for this graph? (Yes or no question)3. Explain your reason of how you know

Answer 1

well, let's find the equation of the line through those points then, and let's see

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

`\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}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \\e ~~ 3x-y = 6`