(3,-4)(5,1)
slope = (1 - (-4) / (5 - 3) = (1 + 4) / 2 = 5/2
y = mx + b
slope(m) = 5/2
use either of ur points (5,1)...x = 5 and y = 1
now we sub and find b, the y int
1 = 5/2(5) + b
1 = 25/2 + b
1 - 25/2 = b
2/2 - 25/2 = b
-23/2 = b
so ur equation is y = 5/2x - 23/2...but we need it in standard form
y = 5/2x - 23/2...subtract 5/2x from both sides
-5/2x + y = -23/2....multiply everything by -2
5x - 2y = 23 <== standard form
