Which of the following is an equation of a line parallel to y-1=2x? A. y=2x+3 B. 3y-3=2x C. y= 2x+3/2 D. y=1/2x-3 E. y=x-2/3?

Consider the given line :
y - 1 = 2x
y = 2x + 1
Then, slope of the given line = 2

A.
y = 2x + 3
Slope of the line = 2
It is equal to the slope of the given line, and thus the line is parallel to the given line.

B.
3y - 3 = 2x
y = (2/3)x + 1
Slope of the line = 2/3
It is NOT equal to the slope of the given line, and thus the line is NOT parallel to the given line.

C.
y = (2x + 3)/2
y = x + (3/2)
Slope of the line = 1
It is NOT equal to the slope of the given line, and thus the line is NOT parallel to the given line.

D.
y = 1/(2x - 3)
It is NOT a straight line.

E.
y = x - (2/3)
Slope of the line = 1
It is NOT equal to the slope of the given line, and thus the line is NOT parallel to the given line.


The answer: A. y = 2x + 3

Parallel line have equal slopes.
Slope is the coefficient of x

y-1=2x
y=2x+1 --- slope 2

A
y=2x+3, slope 2 (yes)

B.
3y-3 = 2x
3y = 2x+3
y = (2/3) x + 1 , slope =2/3 No

C.
y=2x+3/2
yes ; slope = 2

D.
y=1/2 x - 3
no; slope =1/2

E.
y=x -2/3
no, slope = 1

y - 1 = 2x has a slope of 2
(A) and (C) have slopes of 2 so they are parallel lines.

Parallel lines have the same slope.
y-1 = 2x can be rewritten as y = 2x+1 and has a slope of 2.

A. y = 2x+3 has a slope of 2
C. y = 2x + 3/2 has a slope of 2.

So the answer is Options A and C................ANS

A would work. C would also work, unless you meant y = (2x+3)/2.

C