5B Graphing systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function. It can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the solution of a system of linear inequalities represent?

Back

The solution of a system of linear inequalities represents the set of all points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

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 can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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. The solution set is typically the shaded region.

Front

What does the inequality y > -x - 1 represent graphically?

Back

It represents the region above the line y = -x - 1, where all points (x, y) satisfy the inequality.

Front

What is the solution set for the system of inequalities y ≥ x + 4 and y < -x - 1?

Back

The solution set is the region where the graph of y ≥ x + 4 overlaps with the graph of y < -x - 1.

Front

How do you find the intersection of two linear inequalities?

Back

To find the intersection, graph both inequalities and identify the region where their shaded areas overlap.

Front

What does the inequality y < 2x - 4 indicate about the graph?

Back

It indicates that the region below the line y = 2x - 4 is included in the solution set.