Question

Find the slope of the line perpendicular to the line joining the points $(1,7)$ and $(-4,3)$.

Answer 1

We know that the slope of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, the given points are $(1,7)$ and $(-4,3)$, therefore, the slope of the line is:

$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{3-7}{-4-1}=\frac{-4}{-5}=\frac{4}{5}$

We also know that if the slope of the two lines have the relation $m_1\times m_2=-1$, then the lines are perpendicular to each other, therefore, the slope $m_2$ of the line perpendicular to the given line is:

$m_1\times m_2=-1\Rightarrow \frac{4}{5}\times m_2=-1\Rightarrow 4m_2=-5\Rightarrow m_2=-\frac{5}{4}$

Hence, the slope of the line perpendicular to the given line is$-\frac{5}{4}$.