Question

$$\mathrm{A}(2,3)$$ and $$\mathrm{B}(-2,5)$$ are two given points.
Find:

1. the gradient of AB;
2. the equation of AB;
3. the co-ordinates of the point, where AB intersects $$x$$-axis.

Answer 1

i. Gradient of $$AB$$: 

$$m = \frac{5 - 3}{-2 - 2}$$

$$= \frac{2}{-4}$$

$$= -\frac{1}{2}$$

ii. Equation of the line $$AB$$ using point $$A(2, 3)$$: 

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

$$2(y - 3) = -(x - 2)$$

$$2y - 6 = -x + 2$$

$$x + 2y - 8 = 0$$

iii. The line intersects the $$x$$-axis where $$y = 0$$:

$$x + 2(0) - 8 = 0$$

$$\implies x = 8$$

Therefore, the coordinates of the point of intersection with the $$x$$-axis are $$(8, 0)$$.