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 < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, 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 (x, y) that satisfy the inequality.

Front

What is the difference between a solid line and a dashed line in the graph of linear 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

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.

Front

How do you determine if a point is a solution to a linear inequality?

Back

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

Front

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

Back

The boundary line separates the coordinate plane into two regions, one that satisfies the inequality and one that does not.

Front

What does the term 'system of inequalities' mean?

Back

A system of inequalities is a set of two or more inequalities with the same variables that are solved together.

Front

How can you identify the correct system of inequalities from a graph?

Back

Identify the boundary lines and their slopes, then determine the direction of shading to match the inequalities.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.