Question

Am I right?
Which of the following is the equation of a line parallel to the line y=4x+1, passing through the point (5,1)?

A.) 4x-y=19
B.) 4x+y=-19
C.) -4x-y=19
D.)4x+y=19

Is it D?

Answer 1

the line you want has the same slope as the line
y= 4x+1

that is in the form y=mx + b
m is the slope
in this case, m matches up with 4
so the slope is 4

Answer 2

your line will go through the point (5,1)
y = m x + b
but we know m=4, and if x is 5, y is 1
1 = 4*5+b
1=20 + b
b= 1-20= -19

so your line is
y = 4x -19

rearrange to match one of your choices.