Question

A graph of a linear equation passes through ( -2,0) and (0,-6) is the \(3x-y=6\), both ordered pairs solutions for the equation

Answer 1

\(3x-y=6\) (1)
We know that the equatioan passing through \((x_1,y_1) and (x_2,y_2)\) is
\(\displaystyle{y}-{y}_{{1}}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}{\left({x}-{x}_{{1}}\right)}\)
\(\displaystyle{y}-{0}=\frac{{-{6}-{0}}}{{{0}-{\left(-{2}\right)}}}{\left({x}-{\left(-{2}\right)}\right)}\)
\(\displaystyle{y}=-\frac{{6}}{{2}}{\left({x}+{2}\right)}\)
\(\displaystyle{y}=-{3}{\left({x}+{2}\right)}\)
\(\displaystyle{y}=-{3}{x}-{6}\)
\(\displaystyle{3}{x}+{y}+{6}={0}\)
\(\displaystyle{3}{x}+{y}=-{6}{\left({2}\right)}\)
By, equations \((1) + (2)\), we get
\(\displaystyle{3}{x}-{y}={6}\)
\(\displaystyle{3}{x}+{y}=-{6}\)
\(\displaystyle{6}{x}={0}\Rightarrow{x}={0}\)
put value in equation (2), we get
\(\displaystyle{3}{x}+{y}=-{6}\)
\(\displaystyle{3}\times{0}+{y}=-{6}\)
\(\displaystyle{y}=-{6}\)
So, ordered parts (0,-6)