Find the equation of a line parallel to y = -4x + 2 passing through (2,3)
A.
y + 4x + 11 = 0
B.
y - 4x - 11 = 0
C.
y + 4x - 11 = 0
D.
y - 4x + 11 = 0
Correct Answer: y + 4x - 11 = 0
Explanation
By comparing y = mx + c
with y = -4x + 2,
the gradient of y = -4x + 2 is m1 = -4
let the gradient of the line parallel to the given line be m2,
then, m2 = m1 = -4
(condition for parallelism)
using, y - y1 = m2(x - x1)
Hence the equation of the parallel line is
y - 3 = -4(x-2)
y - 3 = -4 x + 8
y + 4x = 8 + 3
y + 4x = 11
y + 4x - 11 = 0
By comparing y = mx + c
with y = -4x + 2,
the gradient of y = -4x + 2 is m1 = -4
let the gradient of the line parallel to the given line be m2,
then, m2 = m1 = -4
(condition for parallelism)
using, y - y1 = m2(x - x1)
Hence the equation of the parallel line is
y - 3 = -4(x-2)
y - 3 = -4 x + 8
y + 4x = 8 + 3
y + 4x = 11
y + 4x - 11 = 0
