#5.6 Graphing Linear Inequalities in Two Variables

Front

What is a linear inequality in two variables?

Back

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). Then shade the region that satisfies the inequality.

Front

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

Back

The shaded region represents all the solutions to the inequality. Any point in this region satisfies the inequality.

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 (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 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 standard form of a linear inequality?

Back

Front

What does the term 'solution set' mean in the context of linear inequalities?

Back

The solution set is the collection of all points (x, y) that satisfy the inequality. It can be represented graphically as the shaded region on the graph.

Front

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

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is solid or dashed. Then, find a test point (usually (0,0) if it is not on the line) to see if it satisfies the inequality, which helps determine the direction of the inequality.

Front

What is the role of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis. It is used to plot the line and can help in determining the equation of the line.