The straight line L₁ passes through the points with coordinates (4, 6) and (12, 2) The straight line L₂ passes through the origin and has gradient -3 The lines L₁ and L₂ intersect at point P - Edexcel - GCSE Maths - Question 19 - 2018 - Paper 2

Using the point-slope form of the line, the equation for L₁ is given by: $y - y_1 = m(x - x_1)$ Substituting the gradient and a point (4, 6):

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

Expanding this:

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

Rearranging gives:

$y = -\frac{1}{2}x + 8$

L₂ passes through the origin (0, 0) with a gradient of -3. The equation of L₂ is thus:

$y = -3x$

To find point P where L₁ and L₂ intersect, set their equations equal:

$-\frac{1}{2}x + 8 = -3x$

Rearranging gives:

$-\frac{1}{2}x + 3x = 8$

This simplifies to:

$\frac{5}{2}x = 8$

Thus,

$x = \frac{8 \cdot 2}{5} = \frac{16}{5} = 3.2$

Substituting $x = 3.2$ into either equation (using L₂):

$y = -3(3.2) = -9.6$

The coordinates of point P are (3.2, -9.6).