Final answer:
The equation of the line that is parallel to y=6x-1 must have the same slope, which is 6. Among the options given, a) y = 6x + 4 has the correct slope and is therefore the parallel line.
Step-by-step explanation:
To find the equation of the line that is parallel to a given line, we need to ensure that the new line has the same slope as the original line. The given equation is y = 6x - 1, so its slope is 6. For two lines to be parallel, they must have the same slope but can have different y-intercepts.
Now, let's examine the options:
- y = 6x + 4: This equation has a slope of 6, which matches the slope of the given line.
- y = -6x - 1: This equation has a slope of -6, which is not the same as 6, so it is not parallel.
- y = 6x - 3: This equation has a slope of 6, which is parallel to the given line, but since there is only one correct answer, we must choose the first option that fits the criteria.
- y = -6x + 1: This equation has a slope of -6, which is the negative of the given line's slope, so it is not parallel.
Therefore, the correct answer is a) y = 6x + 4, as it is the first option that has the correct slope of 6.