Point A has coordinates (-4, 6) and point B has coordinates (8, 3) - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

To find the equation of line AB, we can use the point-slope form of the line equation:

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

Using point A (-4, 6) and the gradient $m = -\frac{1}{4}$:

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

Distributing the gradient:

$y - 6 = -\frac{1}{4}x - 1$

Now, add 6 to both sides to get it into slope-intercept form:

$y = -\frac{1}{4}x + 5$

Thus, the equation of line AB is:

$y = -\frac{1}{4}x + 5$

Since parallel lines have the same gradient, the gradient of the line passing through point P (0, -2) will also be $-\frac{1}{4}$. Using the point-slope form again:

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

For point P (0, -2):

$y - (-2) = -\frac{1}{4}(x - 0)$

Simplifying this gives:

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

Subtracting 2 from both sides yields:

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

Thus, the equation of the line parallel to line AB that passes through P is:

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