Find the equation of a line parallel to y = -4x + 2 passing through (2,3)

Find the equation of a line parallel to y = -4x + 2 passing through (2,3)

Answer Details

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