Linear Inequalities in two variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by <, >, ≤, or ≥ c, where a, b, and c are constants and x and y are variables.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region that satisfies the inequality.

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, which can be visualized as a shaded region on the graph.

Front

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

Back

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

Front

How can you determine if a point is part of the solution set for a linear inequality?

Back

To determine if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What type of line does the inequality x < 2 create when graphed?

Back

The inequality x < 2 creates a solid, vertical line at x = 2, with the region to the left shaded.

Front

What type of line does the inequality y < 2 create when graphed?

Back

The inequality y < 2 creates a solid, horizontal line at y = 2, with the region below shaded.

Front

What does the inequality y > x represent when graphed?

Back

The inequality y > x represents a region above the line y = x, which is a dashed line indicating that points on the line are not included in the solution set.

Front

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

Back

The slope in a linear inequality indicates the steepness and direction of the boundary line, affecting the orientation of the shaded region.

Front

How do you write the equation of a line from a linear inequality?

Back

To write the equation of a line from a linear inequality, convert the inequality into an equation by replacing the inequality sign with an equal sign.