Question

what does a dashed line mean in the graph of an inequality?
choose the correct answer below.
a. a dashed line is used to show that a line is not part of a graph.
b. a dashed line is used to show that a line is part of a graph.
c. a dashed line is used to show the solution region. the line is the collection of all ordered pairs that are not solutions to the system.
d. a dashed line is used to show the solution region. the line is the collection of all ordered pairs that are solutions to the system.

Explanation:

In the graph of an inequality, a dashed line indicates that the points on the line are not part of the solution set (this is for strict inequalities like \( y < mx + b \) or \( y > mx + b \), where the boundary line is not included). Option A states this correctly. Option B is incorrect as a dashed line isn't used to show the line is part of the graph (solid lines do that for non - strict inequalities). Option C is wrong because the dashed line is related to the boundary of the solution region, not the non - solution ordered pairs in that way. Option D is also incorrect as the dashed line's points are not solutions (for strict inequalities), so it doesn't represent the collection of all solutions.

Answer:

A. A dashed line is used to show that a line is not part of a graph.