Question

given two points P(2,1) and Q(4,7).find an equation of the straight line passing through Q and perpendicular to PQ

Answer 1

Slope

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{4-2} = 3$

Perpendicular slope

$m = -\frac{1}{3}$

Passes through (4,7)

$y - y_1 = m(x - x_1)$

$y - 7 = -\frac{1}{3}(x - 4)$

$y = -\frac{1}{3}x + 7 + \frac{4}{3}$

$y = -\frac{1}{3}x + \frac{25}{3}$