Given the point (2, -1) and the line 2y+4x-8=0, what is the line parallel to it and that passes through (2,-1)?

If 2 lines are parallel, their slopes have to be
equal.

We'll put the given equation of the line in the
point slope form.

y = mx +
n

For this reason, we'll have to isolate y to the left side
and we'll subtract 4x both sides:

2y = 8 -
4x

We'll divide by 2:

y = -2x
+ 4

Comparing, we'll get the slope of the first line: m1 =
-2

The slope of the parallel line is m2 =
-2.

The line is passing through the point  (2 , -1). The
equation of the parallel line is:

y + 1 = -2(x -
2)

We'll subtract 1:

y = -2(x
- 2) - 1

We'll remove the
brackets:

y = -2x + 4  -
1

We'll combine like terms:

y
= -2x + 3

The equation of the parallel line
is:

y = -2x +
3