Which choice is the equation of a line that passes through point (7, 3) and is parallel to the line represented by this equation?

y = 2/7x - 3

A. 7x + 3y = 2
B. y = 2/7x + 1
C. y = -7/2x -3
D. 2x + 7y = 1

i would assume that the answer to this would be B, as they both have the same slope. if the y-intercepts were the same, they would be the same line. is this right?

It is

Yes, you are correct! The equation of a line is in the form y = mx + b, where m is the slope and b is the y-intercept.

To determine which equation represents a line parallel to y = (2/7)x - 3 and passes through the point (7, 3), we need to find an equation that has the same slope as the given line.

The slope of the given line is 2/7. Any line parallel to this line will also have a slope of 2/7.

Now we can check the options:

A. 7x + 3y = 2: This equation is not in the form y = mx + b, so we need to convert it. Dividing by 3, we get y = (-7/3)x + 2/3. The slope of this line is -7/3, which is not the same as 2/7. Therefore, it is not parallel to the given line.

B. y = (2/7)x + 1: This equation is already in the form y = mx + b with a slope of 2/7. Since it has the same slope, it is parallel to the given line.

C. y = (-7/2)x - 3: This equation has a slope of -7/2, which is not the same as 2/7. Therefore, it is not parallel to the given line.

D. 2x + 7y = 1: Dividing by 7, we get y = (-2/7)x + 1/7. The slope of this line is -2/7, which is not the same as 2/7. Therefore, it is not parallel to the given line.

Therefore, the correct answer is B. y = (2/7)x + 1, as it has the same slope and passes through the given point (7, 3).