Final answer:
The correct answer is option D (y < 5/2x + 2) because it has a positive reciprocal slope and a different y-intercept compared to the graphed inequality y ≥ -5/2x - 3, which means it will not have a shared solution set.
Step-by-step explanation:
The student is asking which linear inequality will not have a shared solution set with the graphed linear inequality y ≥ -5/2x - 3. To find the inequality without a shared solution set, we compare the slopes and y-intercepts of each option provided with the graphed inequality.
The given graphed inequality has a negative slope and a y-intercept of -3. We are looking for an inequality whose solution set will not overlap with the graphed inequality:
- A. y > 2/5 x + 2 has a positive slope and y-intercept of +2.
- B. y < -5/2x – 7 has a negative slope, like the graphed inequality, but a lower y-intercept.
- C. y > -2/5 x –5 has a positive slope and y-intercept of -5.
- D. y < 5/2x + 2 has a positive slope, and it is the positive reciprocal of the slope of the graphed inequality (-5/2).
Based on the information above, option D is the correct answer because this inequality, with its positive reciprocal slope and different y-intercept, will not share a solution set with the original graphed inequality.