ABCD is a rectangle - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 1

Since ABCD is a rectangle, the slopes of lines AD and BC must be equal and perpendicular to the slopes of lines AB and DC.

Given that the slope of line L is $-\frac{1}{2}$, the slope of line M (which is perpendicular to line L) can be found using the negative reciprocal:

$m = -\frac{1}{\text{slope of L}} = -\frac{1}{-\frac{1}{2}} = 2.$

This implies that the slope of line M is 2.

Using the slope-point form of a linear equation, we can express line M in terms of its slope and any point on it (for example, point A, which we can denote as (0, 6) based on the intersection with line L):

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

Substituting $m = 2$, $(x_1, y_1) = (0, 6)$:

$$y - 6 = 2(x - 0) \ y - 6 = 2x \ y = 2x + 6$$

Thus, the equation of line M is:

$y = 2x + 6$