i. A (x1 , y1 ) = A (2, 3) and B (x2 , y2 ) = B (4, 7)
Here, x1 = 2, x2 = 4, y1 = 3, y2 = 7
Slope of line AB = (y2 - y1)/(x2 - x1)
=(7 - 3)/(4 - 2)
= 4/2 = 2
∴ The slope of line AB is 2.
ii. P (x1 , y1 ) = P (-3, 1) and Q (x2 , y2 ) = Q (5, -2)
Here, x1 = -3, x2 = 5, y1 = 1, y2 = -2
Slope of line PQ = (y2 - y1)/(x2 - x1)
= (-2 - 1)/(5 - (-3))
= -3/(5+3) = -3/8
The slope of line PQ is -3/8
iii. C (x1 , y1 ) = C (5, -2) and D (x2 , y2 ) = D (7, 3)
Here, x1 = 5, x2 = 7, y1 = -2, y2 = 3
Slope of line CD = (y2 - y1)/(x2 - x1)
= (3 - (-2))/ (7 - 5)
= (3 + 2)/2 = 5/2
∴The slope of line CD is 5/2