Linear inequalities (two variables)

Front

What is a linear inequality in two variables?

Back

Front

What does the shaded area represent in a graph of a linear inequality?

Back

The shaded area represents all the possible solutions to the linear inequality. Points in this area satisfy the inequality.

Front

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

Back

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

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is non-strict (≤ or ≥) and excluded if the inequality is strict (< or >).

Front

How can you graph a linear inequality?

Back

1. Graph the boundary line by treating the inequality as an equation. 2. Use a dashed line for strict inequalities and a solid line for non-strict inequalities. 3. Shade the appropriate region based on the inequality.

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Back

Front

Back

Yes, because substituting (1, 4) gives 4 >= -1 + 2, which is true.

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set refers to all the points (x, y) that satisfy the inequality.

Front

Back

Substitute the x and y values of the point into the inequality. If the result is true, then the point is a solution.