Question

Find the gradient of the line that passes through the points (5, 1) and (2, -5)

Answer 1

Change y / change x = gradient
-5 - 1 = -6 2-5 = -3

-6/-3 = 2 so

gradient = 2

Answer 2

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Suppose :

a = ( 5 , 1 ) and b = ( 2 , - 5 )

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We have following equation to find the slope of the line using two points :

$slope = \frac{y(b) - y(a)}{x(b) - x(a)}$

Now just need to put the coordinates in the above equation ;

$slope = \frac{ - 5 - 1}{2 - 5}$

$slope = \frac{ - 6}{ - 3}$

Negatives simpliflies

$slope = \frac{6}{3}$

$slope = \frac{3 \times 2}{3}$

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

$slope = 2$

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