Question

Find the equation of a line that has Y-intercept 3 units and is perpendicular to the line joining (2, – 3) and (4, 2).

Answer 1

Let m be the slope of required line
Slope of the given line = ${\displaystyle \frac{2+3}{4-2}=\frac{5}{2}}$.
But the required line is perpendicular to the given line.
Hence,
m x Slope of the given line = -1
⇒ m x ${\displaystyle \frac{5}{2}}$ = -1
⇒ m = ${\displaystyle \frac{-2}{5}}$
Y-intercept, c = 3
Hence, equation of the required line is given by
y = mx + c
i.e., y = ${\displaystyle -\frac{2}{5}x+3}$
⇒ 5y = -2x + 15
⇒ 2x + 5y - 15 = 0.