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

Answer: Option C

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