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 (>, <, ≥, ≤) instead of an equal sign.

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

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 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 make the inequality true, represented graphically as a shaded region on the graph.

Front

If a student must be at least 15 years old to obtain a driver’s permit, how is this represented as an inequality?

Back

This is represented as a ≥ 15.

Front

What is the cost for an adult in the gymnastics organization problem?

Back

The cost for an adult is $240.

Front

What is the cost for a child in the gymnastics organization problem?

Back

The cost for a child is $150.

Front

If a local gymnastics organization has $3200, what is the inequality that represents the total cost for adults (a) and children (c)?

Back

240a + 150c ≤ 3200.

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, it means that the point satisfies the equation of the line, and whether it is included in the solution set depends on the type of inequality (solid line for ≤ or ≥, dashed line for < or >).

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, then the point is a solution.