Final answer:
To be parallel to the line y = 7/3x + 2, an equation must have the same slope but a different y-intercept. The equations that match this criterion and therefore are parallel are (B) y = 7/3x - 5 and (D) y = 7/3x + 5.
Step-by-step explanation:
To determine which equation is parallel to the given line, y = 7/3x + 2, we need to look for an equation that has the same slope but a different y-intercept. The slope of the given line is 7/3. For two lines to be parallel, they must have identical slopes and different y-intercepts. Therefore, we need to find the equation among the options that have a slope of 7/3 and a different y-intercept than the given line.
- A) y = 2x + 5: This equation has a different slope of 2, so it's not parallel.
- B) y = 7/3x - 5: This equation has the same slope of 7/3, but a different y-intercept of -5, making it parallel to the given line.
- C) y = -7/3x + 2: This equation has a slope of -7/3, which is the negative reciprocal of our given line's slope, indicating that it's perpendicular, not parallel.
- D) y = 7/3x + 5: This equation, like option B, has the same slope of 7/3. However, it's still considered parallel since the y-intercept is different (5 in this case).
Based on the definition of parallel lines, the correct answers are B) y = 7/3x - 5 and D) y = 7/3x + 5.