Graphing Linear Inequalities

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 such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

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 (above the line for '>' or '≥', and below the line for '<' or '≤').

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 do 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 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, represented graphically as a shaded region on the coordinate plane.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line of a linear inequality, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).

Front

How can 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, observe the shaded region to see if it is above or below the line, which will help you choose the correct inequality symbol.

Front

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

Back