Graph 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

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, often visualized as a shaded region on a graph.

Front

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

Back

A solid line indicates that points on the line are included in the solution set (≤ or ≥), while a dotted 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 part of the solution set.

Front

What does shading above a line indicate when graphing a linear inequality?

Back

Shading above a line indicates that the solution set includes all points where the y-value is greater than the y-value on the line (y > mx + b).

Front

What does shading below a line indicate when graphing a linear inequality?

Back

Shading below a line indicates that the solution set includes all points where the y-value is less than the y-value on the line (y < mx + b).

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dotted line, then shade below the line to represent all points where y is less than 2x + 3.

Front

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

Back

The boundary line separates the solution set from the non-solution set; points on the line may or may not be included based on the type of inequality.

Front

What is the solution to the inequality y > -x + 1?

Back

The solution includes all points above the line y = -x + 1, excluding the line itself.

Front

How can you check if a point lies in the solution set of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality is satisfied, the point lies in the solution set.