When graphing $3x + 5y > 20$, the boundary line is
A. solid
B. dotted
Answer (1)
The inequality is 20"> 3 x + 5 y > 20 .
Because the inequality is strict ( "> > ), the boundary line is not included in the solution.
Therefore, the boundary line is dotted.
The boundary line is dotted .
Explanation
Understanding the Inequality The given inequality is 20"> 3 x + 5 y > 20 . We need to determine whether the boundary line is solid or dotted when graphing this inequality.
Analyzing the Inequality Sign The inequality 20"> 3 x + 5 y > 20 does not include the equals sign. This means that the points on the line 3 x + 5 y = 20 are not part of the solution set.
Boundary Line Convention When graphing inequalities, a strict inequality ( "> > or < ) is represented with a dotted line to indicate that the points on the line are not included in the solution. A non-strict inequality ( ≥ or ≤ ) is represented with a solid line to indicate that the points on the line are included in the solution.
Conclusion Since the inequality is 20"> 3 x + 5 y > 20 , which is a strict inequality, the boundary line is dotted.
Examples
Imagine you're planning a party and have a budget constraint. If you can spend more than $200 on decorations and food, but not exactly $200 (because you want a buffer), the boundary representing your spending limit would be dotted on a graph. This dotted line visually reminds you that you need to stay above, but not on, that specific spending limit. This concept applies to various real-world scenarios, such as resource allocation, setting limits, and defining acceptable ranges in manufacturing or quality control.
