Write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:
part a) passes through (2, 5) and m = 3/4
part b) passes through (−3, 2) and (1, −3)
part c)m=2/5 and y-intercept =-6
part d) x-intercept = 4 and y-intercept = −2
part e) passes through (−2, 2) and parallel to 4x − 3y − 7 = 0

Part A) Passes through (2, 5) and m = 3/4

y - 5 = 3/4 (x - 2)

y = 3x/4 - 3/2 + 5

y = 3x/4 + 7/2

Part B) Passes through (−3, 2) and (1, −3)

y - 2 = [(2 -(-3)) / (-3 -1) ] * [x - (-3)]

y - 2 = [5/(-4)] * [x+3]

y = -5x/4 - 15/4 + 2

y = -5x/4 -7/4

Part C)m=2/5 and y-intercept =-6

y = 2x/5 - 6

Part D) x-Intercept = 4 and y-intercept = −2

x-Intercept = 4 = (4,0)

and y-intercept = −2 = (0, - 2)

y - (-2) = [ (0 - (-2) ) / (4-0)] * [x-0]

y +2 = [2/4] (x)

y = x/2 - 2

Part E) Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0

Parallel lines have same slope, m.

m = 4/3

y  - 2 = 4/3 (x - (-2))

y - 2 = 4x/3 + (4)(2)/3

y = 4x/3 +8/3 + 2

y = 4x/3 + 14/3