Question

Are the lines with equations $2x-3y=8$ and $-x+4y=2$ parallel, perpendicular or neither?

Answer 1

Since the two lines are parallel if their slopes are identical that is $m_1=m_2$ and two lines are perpendicular if $m_1{\times m}_2=-1$.

Consider the first line that is

$2x-3y=8$ or

$-3y=-2x+8$ or

$y=\frac{2}{3}x-\frac{8}{3}$

Therefore, $m_1=\frac{2}{3}$

Now consider the second line that is

$-x+4y=2$

$\Rightarrow 4y=x+2$

$\Rightarrow y=\frac{1}{4}x+\frac{1}{2}$

Therefore, $m_2=\frac{1}{4}$

Since $m_1{\ne m}_2$ and also $m_1{\times m}_2\ne -1$, hence, the two given lines are neither parallel nor perpendicular.