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).
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