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'?

Answer: Option A

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)
$$\begin{array}{rl}& \therefore \frac{y_2-y_1}{x_2-x_1}=m_2\\ & \Rightarrow \frac{3-a}{4-5}=-6\\ & \Rightarrow 3-a=+6\times +1\\ & \therefore a=-3\end{array}$$