Find the gradient of a line passing through the following pairs of points :

(i) (0, -2), (3, 4)

(ii) (3, -7), (-1, 8).

(i) Gradient of a line = $\dfrac{y$2 - y1}{x2 - x1}

Putting values in above formula we get,

$\text{Gradient } = \dfrac{4 - (-2)}{3 - 0} \\[1em] = \dfrac{6}{3} \\[1em] = 2.$

Hence, the gradient of the line passing through (0, -2), (3, 4) is 2.

(ii) Gradient of a line = $\dfrac{y$2 - y1}{x2 - x1}

Putting values in above formula we get,

$\text{Gradient } = \dfrac{8 - (-7)}{-1 - 3} \\[1em] = \dfrac{15}{-4} \\[1em] = -\dfrac{15}{4}.$

Hence, the gradient of the line passing through (3, -7), (-1, 8) is $-\dfrac{15}{4}$.