When graphing $y<\frac{-2}{5} x+1$, the boundary line is
A. dotted
B. solid
Answer (1)
The inequality is y < 5 − 2 x + 1 .
The inequality symbol is ' < ', indicating a strict inequality.
Strict inequalities are graphed with a dotted boundary line.
Therefore, the boundary line is d o tt e d .
Explanation
Understanding the Inequality The given inequality is y < 5 − 2 x + 1 . We need to determine whether the boundary line should be dotted or solid when graphing this inequality.
Analyzing the Inequality Symbol The inequality symbol is ' < ', which means 'less than'. This indicates that the points on the line y = 5 − 2 x + 1 are not included in the solution set.
Dotted vs. Solid Line When graphing inequalities, a strict inequality (like < or "> > ) is represented with a dotted line to show that the points on the line are not part of the solution. A non-strict inequality (like ≤ or ≥ ) is represented with a solid line to show that the points on the line are included in the solution.
Conclusion Since our inequality is y < 5 − 2 x + 1 , the boundary line is dotted.
Examples
Imagine you're drawing a map to a hidden treasure. The inequality y < 5 − 2 x + 1 defines the area where the treasure is buried. Because the boundary line is dotted, it means you can't dig exactly on that line; the treasure is somewhere strictly within the defined area, not on its edge. This concept is useful in various real-world scenarios, such as defining safe operating zones for machinery or determining acceptable ranges for measurements in experiments. Understanding whether a boundary is inclusive (solid line) or exclusive (dotted line) is crucial for making accurate decisions.
