Answer:
5x - 2y - 16 = 0
Explanation:
The original ecuation is:
5x - 2y = 2
5x - 2 = 2y
2y = 5x - 2
y = (5x - 2) / 2
y = 5x/2 - 2/2
y = 5x/2 - 1
The slope of this line is 5/2.
The condition of parallelism is:
m1 = m2So, both lines have the same slope.
The parallel line must pass through the point P(2, -3).
Using the ecuation point-slope
y - y1 = m(x - x1)
y - (-3) = (5/2)(x - 2)
y + 3 = 5/2(x - 2)
2(y + 3) = 5(x - 2)
2y + 6 = 5x - 10
2y + 6 - 5x + 10 = 0
-5x + 2y + 16 = 0
5x - 2y - 16 = 0