2-Variable Equations & Inequalities Online Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Max is given the graph of the linear inequality 3x−7.2y<0
and asked to determine whether a given point is a solution. She notices that the point falls on the boundary line of the graph. What should she conclude?(1 point)
Responses

The point is not a solution to the linear inequality because points on boundary lines are never solutions to linear inequalities.
The point is not a solution to the linear inequality because points on boundary lines are never solutions to linear inequalities.

The point is a solution to the linear inequality because points on boundary lines are always solutions to linear inequalities.
The point is a solution to the linear inequality because points on boundary lines are always solutions to linear inequalities.

The point is a solution to the linear inequality because points on boundary lines are only solutions when the inequality symbol is >
or <
.
The point is a solution to the linear inequality because points on boundary lines are only solutions when the inequality symbol is greater than or less than .

The point is not a solution to the linear inequality because points on boundary lines are only solutions when the inequality symbol is ≥
or ≤
.
The point is not a solution to the linear inequality because points on boundary lines are only solutions when the inequality symbol is greater-than-or-equal-to or less-than-or-equal-to .
Remaining Attempts : 3
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Answer 1

To analyze the inequality \(3x - 7.2y < 0\), we first determine the boundary line by setting the equation equal to zero: \(3x - 7.2y = 0\). This line divides the plane into two halves.

In the case of strict inequalities (like "<" or ">"), points that lie on the boundary line are not considered solutions to the inequality.

Since the given inequality is \(3x - 7.2y < 0\), and Max noticed that the point falls on the boundary line, she should conclude:

The point is not a solution to the linear inequality because points on boundary lines are never solutions to linear inequalities.

So, this would be the correct response.