Find the equation of the line passes through ( -3, 4) and parallel to the line 2y-4x + 2 = 0

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 add 4x and subtract 2 both sides:

2y = 4x -
2

We'll divide by 2:

y = 2x -
1

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  (-3 , 4). The
equation of the parallel line is:

y - 4 = 2(x +
3)

We'll add 4:

y = 2(x + 3) +
4

We'll remove the brackets:

y
= 2x + 6  + 4

We'll combine like
terms:

y = 2x +
10

The equation of the parallel line is:

y = 2x +
10