Linear inequalities (two variables)

Front

What is a linear inequality in two variables?

Back

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 to a linear inequality, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

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

Back

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

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

How can you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for strict inequalities) or a solid line (for non-strict inequalities). Then shade the appropriate area based on the inequality.

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 of a linear inequality, it is a solution if the inequality is non-strict (≤ or ≥) but not a solution if the inequality is strict (< or >).

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, which can be represented graphically as a shaded region on a coordinate plane.

Front

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

Back

To test if a point is a solution, substitute the coordinates of the point into the inequality. If the resulting statement is true, then the point is a solution.

Front

What is the significance of the coefficients in a linear inequality?

Back

The coefficients in a linear inequality determine the slope and position of the boundary line, affecting the direction of the shading in the graph.

Front

What is an ordered pair in the context of linear inequalities?

Back

An ordered pair (x, y) represents a specific point on the coordinate plane, where x is the horizontal coordinate and y is the vertical coordinate.