Find the equation of the line passes through the point ( 5,-2) and parallel to the line : 2y-x = 5

Two lines are parallel if and only if their slopes are
equal or if the ratio of their correspondent coefficients are also
equal.

We'll put the given equation into the standard form.
For this reason, we'll isolate 2y to the left side:

2y = x
+ 5

We'll divide by 2:

y = x/2
+ 5/2

We'll write the standard form of the equation of the
parallel line and we'll identify the value of the slope for both
lines.

y = mx + n

m1 = 1/2 and
m2 = m

The slopes have like
values.

m = 1/2

Now, we'll
write the equtaion of the line that has the slope m=1/2 and it passes through the point
(5,-2).

y - (-2) = (1/2)(x -
5)

y + 2 = x/2 - 5/2

y = x/2
- 5/2 - 2

y = x/2 - 9/2

2y = x
- 9

2y - x + 9 =
0

The equation of the parallel line whose
slope is m = 1/2 and it is passing through the point (5,-2) is 2y - x + 9 =
0.