$A (2, 3)$ and $B (- 2, 5)$ are two given points.
Find: (i) the gradient of $A B$ ;
(ii) the equation of $A B$ ;
(iii) the co-ordinates of the point, where $A B$ intersects x-axis.

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Solution

(1) Gradient $= \frac{5 - 3}{- 2 - 2}$

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

(2) Equation of $A B :$

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

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

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

(3) $A B$ intersects $x -$ axis

Hence $y = 0$

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

So, $x = 8$

The points are $(8, 0)$

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