If the points with coordinates (a , b) and (c , d) lie on the the

Use the coordinates of the two points on the line to find the slope m of the line. 

m = (d – b) / (c – a) 

The slope m of the line can also be calculated using the equation of the line rewritten in the form y = m x + k. 

2 y + 3 x = 4 can be written as 2y = – 3x + 4 

Divide all terms by 2 to obtain y = (-3/2) x + 2 

The slope m is equal to -3 / 2 

Equate the expression of the slope found above to -3 / 2 

-3 / 2 = (d – b) / (c – a) 

Use the above to find d – b 

d – b = -3 / 2 (c – a) = (-3 / 2)(-(a – c)) = 9 / 2 

Answer: 9 / 2