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

Question
Linear equations and graphs

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

2020-12-04

$$3x-y=6$$ (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)

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