Final answer:
The equation parallel to y = 2(x + 3) with no points in common is c. y = 2x - 3 as it has the same slope but a different y-intercept.
Step-by-step explanation:
To find which equation is parallel to the given linear equation y = 2(x + 3), we must identify an equation with the same slope but a different y-intercept. The given equation simplifies to y = 2x + 6, indicating a slope of 2. A parallel line must also have a slope of 2 but cannot have the same y-intercept.
- a. y = x + 6 is not parallel; the slope is 1.
- b. y = -2x - 6 is not parallel; the slope is -2, which is the negative reciprocal.
- c. y = 2x - 3 is parallel, having a slope of 2 and a different y-intercept (-3).
- d. y = 2x + 6 is not an option as it is the same as the given equation.
Therefore, the correct answer is c. y = 2x - 3 as it is the only equation that is parallel to the given equation and has no points in common due to the different y-intercept.