What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?

y = –one-fourthx + 33
y = –one-fourthx + 36
y = 4x − 16
y = 4x + 16

Option D

The equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32) is y = 4x + 16

Solution:

Given that the line passes through point (4, 32)

The line is parallel to y − 1 = 4(x + 3) ---- eqn 1

First let us find the slope of line

The general form of point slope form of line is given as:

 ----- eqn 2

Where "m" is the slope of line

Comparing the eqn 2 with eqn1  y − 1 = 4(x + 3)

We get "m" = 4

The slopes of parallel lines are always equal

Hence the slope of line passing through (4, 32) has the same slope "m" = 4

Now plug in "m" = 4 and in eqn 2 to get the required equation of line

y - 32 = 4(x - 4)

y - 32 = 4x - 16

y = 4x - 16 + 32

y = 4x + 16

Thus the equation of line parallel to given line is y = 4x + 16