5A Graphing systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

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

Front

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

Back

The shaded area represents all the solutions to the inequality, indicating where the values of x and y satisfy the inequality.

Front

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

Back

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

Front

How can 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, then the point is a solution.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set of a system of linear inequalities is the region where the shaded areas of all inequalities overlap on the graph.

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 line is solid (≤ or ≥) and not included if the line is dashed (< or >).

Front

How do you write the inequality for a given graph?

Back

To write the inequality for a graph, identify the slope and y-intercept of the boundary line, then determine the direction of the shading to decide whether to use <, >, ≤, or ≥.

Front

What is the slope-intercept form of a linear equation?

Back

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps to determine the starting point of the graph.