Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be written 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?

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 it mean if a point is part of the solution set of a linear inequality?

Back

A point is part of the solution set if it satisfies the inequality when the coordinates are substituted into the inequality.

Front

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

Back

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

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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, the point is a solution.

Front

What does the term 'boundary line' refer to in the context of linear inequalities?

Back

The boundary line is the line that represents the equation of the linear inequality, separating the solution set from the non-solution set.

Front

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

Back

The slope indicates the steepness of the boundary line and the direction of the shading in the graph, showing how y changes with respect to x.

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 and is used to plot the boundary line of the inequality.

Front

How do you test a point to see if it is in the solution set?

Back

Choose a test point not on the boundary line (commonly (0,0) if it is not on the line) and substitute its coordinates into the inequality.