Find the slope of the line that contains the points named. a(3, 2), b(7, 8)

Lets first find the slope of the line passing through those points. A(3, 2), B(7, 8) all we have to do is divide the y portion over the x segment:
m = (8 - 2)/(7 - 3) = 6/4
m = 3/2
that is the slope of the line
And now lets use the line equation for slope and one point A(3, 2)
y - y1 = m(x - x1), where x1, y1 are the coordinates of a point of the line, A in this case:
y - 2 = (3/2)(x - 3)
y = (3/2)x - 9/2 + 2
y = (3/2)x - 5/2