Graphing Linear Inequalities Test

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid 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 lies in the shaded region of the graph, meaning it satisfies 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 (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does the inequality y > 1/2x + 2 represent graphically?

Back

It represents the region above the line y = 1/2x + 2, not including the line itself.

Front

What is the solution set of a linear inequality?

Back

The solution set is the collection of all points that satisfy the inequality, represented graphically by the shaded region.

Front

How do you write an inequality from a graph?

Back

Identify the boundary line and the direction of shading to determine the inequality symbol and the relationship between the variables.

Front

What does the inequality 3x - y > 4 mean?

Back

It means that the region above the line represented by the equation 3x - y = 4 is the solution set.

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, which helps in graphing the inequality.