The point A(−6, 4) and the point B(8, −3) lie on the line L - Edexcel - A-Level Maths Pure - Question 5 - 2008 - Paper 2

To find the equation of the line L passing through the points A(−6, 4) and B(8, −3), we first calculate the slope (m) using the formula:

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

With the slope known, we can use point-slope form to find the equation of the line. Using point A:

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

This gives us:

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

Expanding this, we find:

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

To write this in the standard form ax + by + c = 0, we rearrange:

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

Multiplying through by 2 to eliminate the fraction, we obtain:

$x + 2y - 2 = 0$

Thus, an acceptable equation for L in integer form is:

$x + 2y - 2 = 0$