3x + 2y = 7 is equivalent to

2y = 7 - 3x divide both sides by 2

y = 7/2 - (3/2)x

y = - (3/2)x + 7/2

the slope is (-3/2).

another way to calculate the slope is using the formula:

m = (y2 - y1)/(x2 - x1) where (x1, y1) and (x2, y2) are point from the line 3x + 2y = 7

for x1 = 0, y1 = 7/2

for x2 = 1, y2 = 2

m = (2 - 7/2)/(1 - 0)

m = (4 - 7)/2

m = -3/2

the slope is -3/2.