# parallel linesknowing the point (2, -1) and the line 2y+4x-8=0, find the line parallel to it and that passes through (2,-1).

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Two parallel lines have equal slopes. The slope of the line 2y + 4x - 8 = 0 can be found by writing it in the form y = mx + c where m is the slope.

2y + 4x - 8 = 0

=> 2y = -4x + 8

=> y = -2x + 4

The slope of the required line is also -2 and it passes through (2, -1), this gives (y + 1)/(x - 2) = -2

=> y + 1 = -2x + 4

=> y + 2x - 3 = 0

**The required line is y + 2x - 3 = 0**

We know that 2 lines are parallel when their slopes are 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).

We'll write the equation of the parallel line that is passing through the point (2 , -1):

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**