#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 it mean if a point is a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it satisfies the inequality when the coordinates of the point are substituted into 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 an inequality?

Back

To determine if a point is a solution, substitute the x and y coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

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

Back

Front

What does the slope of a line represent in a graph?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept of a line?

Back

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 the slope and y-intercept, and decide which side of the line is shaded to determine the inequality symbol.

Front

What is the significance of the shaded region in the graph of a linear inequality?

Back

The shaded region in the graph of a linear inequality represents all the possible solutions to the inequality.