The gradient or slope of a line can be calculated using the given formula: (y2 - y1) / (x2 - x1). Let's apply this formula to compute the gradients of the given pairs of points.
(i) For the first pair of points, (0, -2) and (3, 4):
Step 1: Assign the coordinates as follows: x1 = 0, y1 = -2 and x2 = 3, y2 = 4
Step 2: Apply the formula to find the gradient: gradient = (y2 - y1) / (x2 - x1) = (4 - (-2)) / (3 - 0) = 6 / 3
So, the gradient of the line that passes through the 1st pair of points is 2.0.
(ii) For the second pair of points, (3, -7) and (-1, 8):
Step 1: Again assign the coordinates as follows: x1 = 3, y1 = -7 and x2 = -1, y2 = 8
Step 2: Apply the formula to find the gradient: gradient = (y2 - y1) / (x2 - x1) = (8 - (-7)) / (-1 - 3) = 15 / -4
So, the gradient of the line that passes through the 2nd pair of points is -3.75.
Hence, the gradients for the pair of points (0,−2) and (3,4) and for the pair of points (3,−7) and (-1,8) are 2.0 and -3.75, respectively.