Linear Inequalities & Testing Points

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

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Back

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What does the inequality @@y eq 3x + 7@@ imply about the line?

Back

It implies that the line is not included in the solution set, meaning points on the line do not satisfy the inequality.

Front

How can you tell if a point is above or below a line in a graph?

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A point is above the line if its y-coordinate is greater than the y-value of the line at the same x-coordinate; it is below if the y-coordinate is less.

Front

What is the solution set of the inequality @@y eq 3x + 7@@?

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Front

What does the term 'testing points' mean in the context of linear inequalities?

Back

Testing points refers to the method of selecting specific points to determine whether they satisfy the inequality and help identify the solution region.