Answer: y = -(5/3)x + 8
I assume (6,-2)(6,−2) is actually just (6,−2).
Explanation:
A parallel line will have the same slope as the reference line. Rewite the reference line equation into y=mx+b format:
5x+3y=6
3y = -5x+6
y = -(5/3)x + 6
The parallel line we want will have the same slope, -(5/3):
y = -(5/3)x + b
b will be different since we want this new, parallel, line to go through point (6,-2), so it must be moved to accomodate this point. Find the value of b we need by entering the point into the new equation and solving for b.
y = -(5/3)x + b for point (6,-2)
-2 = -(5/3)(6) + b
-2 = -10 + b
b = 8
y = -(5/3)x + 8