Question

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 = –x + 33
y = –x + 36
y = 4x − 16
y = 4x + 16

Answer 1

Your answer should be
D) Y=4x+16

Answer 2

we know that

if two lines are parallel, then their slopes are equal

in this problem we have

$y-1=4(x+3)$

the slope of the given line is $m=4$

so

with

$m=4$

$point (4.32)$

Find the equation of the line

$y-y1=m(x-x1)$

substitute the values

$y-32=4(x-4)\\y=4x-16+32\\y=4x+16$

therefore

the answer is

$y=4x+16$