Question

How do you know If two lines are perpendicular $?$

Answer 1

Finding if two lines are perpendicular:

Any two lines are perpendicular if their slopes are negative reciprocals.

Formula for the slope of the perpendicular, ${\mathrm{m}}_1=\frac{-1}{{\mathrm{m}}_2}$

where ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are slopes of two lines.

Let's consider another set of equations.

$\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{3}\mathbf{}\mathbf{,}\mathbf{}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{10}$

On comparing $\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{3}\mathbf{}\mathbf{,}\mathbf{}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{10}$ with $\mathit{y}\mathbf{=}\mathit{m}\mathit{x}\mathbf{+}\mathit{c}$

The slopes are ${\mathit{m}}_{\mathbf{1}}\mathbf{=}\mathbf{2}\mathbf{}\mathbf{,}\mathbf{}{\mathit{m}}_{\mathbf{2}}\mathbf{=}\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}}$

If the slope of one line is the negative reciprocal of the second line then, lines are perpendicular .

Hence , both the lines are perpendicular.