Question

How do you write an equation in standard form for a line which passes through $(-6,-7)\mathrm{and}m=-1$?

Answer 1

Determine the equation of the line in standard form which passes through $\mathbf{(}\mathbf{-}\mathbf{6}\mathbf{,}\mathbf{-}\mathbf{7}\mathbf{)}$ and $\mathit{m}\mathbf{=}\mathbf{-}\mathbf{1}$:

The point-slope formula is $y-y_1=m\left(x-x_1\right)$ where $\left(x_1,y_1\right)$ represents the point lie on the line and $m$ represents the slope of a line.

The standard equation of a line is $Ax+By+C=0$.

$$\begin{gathered} y-\left(-7\right)=-1\left(x-\left(-6\right)\right) \\ \Rightarrow y+7=-1\left(x+6\right) \\ \Rightarrow y+7=-x-6 \\ \Rightarrow y+7+x+6=0 \\ \Rightarrow x+y+13=0 \end{gathered}$$

Hence, the equation of the line in standard form passes through $\mathbf{(}\mathbf{-}\mathbf{6}\mathbf{,}\mathbf{-}\mathbf{7}\mathbf{)}$ and $\mathit{m}\mathbf{=}\mathbf{-}\mathbf{1}$ is $\mathit{x}\mathbf{+}\mathit{y}\mathbf{+}\mathbf{13}\mathbf{=}\mathbf{0}$.