The point A (−6, 4) and the point B (8, −3) lie on the line L - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 2

To find the equation of the line L, we first calculate the slope (m) using the points A and B:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 4}{8 - (-6)} = \frac{-7}{14} = -\frac{1}{2}$

Now, we can use the point-slope form of the line equation:

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

Using point A (−6, 4):

$y - 4 = -\frac{1}{2}(x + 6)$
$y - 4 = -\frac{1}{2}x - 3$
$y = -\frac{1}{2}x + 1$

To convert to the form ax + by + c = 0:

$\frac{1}{2}x + y - 1 = 0$

Multiplying through by 2 to eliminate the fraction:

$x + 2y - 2 = 0$

Thus, the equation is:

$x + 2y - 2 = 0$