The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

Slope of the line = $\dfrac{y$2 - y1}{x2 - x1}

Slope of line passing through A and B is m₁,

$= \dfrac{b - 3}{4 - (-2)} \\[1em] = \dfrac{b - 3}{6}.$

The equation of other line is,

⇒ 2x - 4y = 5

⇒ 4y = 2x - 5

⇒ y = $\dfrac{2}{4}x - \dfrac{5}{4}$

⇒ y = $\dfrac{1}{2}x - \dfrac{5}{4}$

Comparing the equation with y = mx + c we get,

slope = m₂ = $\dfrac{1}{2}$

As lines are perpendicular to each other, we have

$\Rightarrow m$1 \times m2 = -1 \\[1em] \Rightarrow \dfrac{b - 3}{6} \times \dfrac{1}{2} = -1 \\[1em] \Rightarrow \dfrac{b - 3}{12} = -1 \\[1em] \Rightarrow b - 3 = -12 \\[1em] \Rightarrow b = -12 + 3 \\[1em] \Rightarrow b = -9.

Hence, the value of b is -9.