Find the equation of the line passing through the point P
Question:

Find the equation of the line passing through the point P( – 3, 5) and perpendicular to the line passing through the points A(2, 5) and B( – 3, 6)

Solution:

As two points passing through line perpendicular to the line are given, we will calculate slope using two points. Let slopes of the two lines be m1 and m2.

$\mathrm{m}_{1}=\frac{\mathrm{y}_{2-\mathrm{y}_{1}}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{6-5}{-3-2}=-\frac{1}{5}$

$\mathrm{~m}_{1}=-\frac{1}{5}$

Now the slope of the equation can be found using

$\mathrm{m}_{1} \mathrm{~m}_{2}=-1$ where $\mathrm{m}_{1}, \mathrm{~m}_{2}$ are slopes of two perpendicular lines

$\frac{-1}{5} \cdot m_{2}=-1 \Rightarrow m_{2}=5$

Using slope – intercept form we will find intercept for line passing through ( – 3, 5)

$y=m x+c$ ……………………….(1)

$5=5(-3)+c$

$c=5+15$

$c=20$

Putting value in equation (1)

$y=5 x+20$

$5 x-y+20=0$

So, the required equation of line 5x – y + 20 = 0.