The line passing through the point (5, a) and point (4, 3) is perpendicular to the line x - 6y = 8. What is the value of 'a'?

Solution (By Examveda Team)

Given,
Equation of line x - 6y = 8
we write it as
$$y = \frac{x}{6} - \frac{8}{6}$$
∴ y = mx (where m is a slope)
∴ m₁ = $$\frac{1}{6}$$
If lines are perpendicular then product of their slopes is equal to -1
m₁ × m₂ = -1
∴ $$\frac{1}{6}$$ × m₂ = -1
m₂ = - 6
∴ Slope of perpendicular line = - 6
Perpendicular line which passes through the points (5, a) and (4, 3)
$$\eqalign{ & \therefore \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = {m_2} \cr & \Rightarrow \frac{{3 - a}}{{4 - 5}} = - 6 \cr & \Rightarrow 3 - a = + 6 \times + 1 \cr & \therefore a = - 3 \cr} $$