Question

Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

Answer 1

The slope of the line joining the points (2, 5) and (3, 6) is:
$m=\frac {6-5}{-3-2}=\frac {1}{-5}$
We know that two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
Therefore, slope of the line perpendicular to the line through the points (2, 5) and (3, 6) is:
$=-\frac 1m=-\frac {1}{(-\frac 15)}=5$
Now, the equation of the line passing through point (-3, 5), whose slope is 5, is:
$(y-5)=5(x+3)$
$y-5=5x+15$
i.e., $5x-y+20=0$