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)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the line 2y + 4x - 8 = 0.

Now the equation of a line parallel to it is 2y + 4x +r=0.

As the parallel line passes through (2, -1)

=> 2y + 4x +r=0

=> 2*-1 + 4*2 + r = 0

=> -2 + 8 + r = 0

=> 6 + r = 0

=> r = -6

Therefore the required equation is 2y + 4x - 6 =0

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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