The line passing through (-2, 5) and (6, b) is perpendicular to the line 20x + 5y = 3. Find b?

Solution (By Examveda Team)

Equation of given line
$$\eqalign{ & \Rightarrow 20x + 5y = 3 \cr & \Rightarrow 5y = 3 - 20x \cr & \Rightarrow y = - 4x + \frac{3}{5} \cr} $$
Slope of line, m₁ = -4
If two are lines are ⊥ then the product of their slope = -1
$$\eqalign{ & {m_1} \times {m_2} = - 1 \cr & - 4 \times {m_2} = - 1 \cr & {m_2} = \frac{1}{4} \cr} $$
Lines passing through the points (-2, 5) and (6, b)
Therefore,
$$\eqalign{ & {\text{Slope}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{b - 5}}{{6 + 2}} = \frac{{b - 5}}{8} \cr & {\text{According to the question,}} \cr & \frac{{b - 5}}{8} = \frac{1}{4} \cr & b - 5 = 2 \cr & \therefore b = 7 \cr} $$