Question

Find the equation of line which is perpendicular to line segment joining (4,2) and (3,5) and cuts of an intercepts -3 on y-axis

Answer 1

First, we have to find slope of second line,
so, we have formula
m1 = (y2-y1) / (x2-x1)
putting values
(4,2) = (x1,y1) and (3,5) = (x2,y2)
m1 = -3
so, when two lines are perpendicular,
m1 × m2 = -1
-3 × m2 = -1
m2 = 1/3
Now, we have slope of line, as well as point it passes through which is (0,3) y intercept.
by using formula,
y - y1 = m (x - x1)
y - 3 = 1/3 (x - 0)
3y - 9 = x
x - 3y + 9 = 0
so, equation of line is x - 3y + 9 = 0.