The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a. - Edexcel - GCSE Maths - Question 19 - 2018 - Paper 1

The equation of the line is given as 3x + 2y = 7. We can rewrite this in slope-intercept form (y = mx + b):

$2y = -3x + 7$ $y = -\frac{3}{2}x + \frac{7}{2}$

Thus, the slope of the given line is (-\frac{3}{2}).

The slope of a line perpendicular to another is the negative reciprocal. Therefore, the slope of line PQ should be:

$m_{PQ} = \frac{2}{3}$

Equating the slopes:

$\frac{b - 4}{a - 3} = \frac{2}{3}$

Cross multiplying gives:

$3(b - 4) = 2(a - 3)$

Expanding this leads to:

$3b - 12 = 2a - 6$

Solving for b:

$3b = 2a + 6$ $b = \frac{2a + 6}{3}$