Graphing Linear Inequalities and Systems of 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 (e.g., <, >, ≤, ≥).

Front

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

Back

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

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

How do you graph the inequality y < 3x + 2?

Back

Graph the line y = 3x + 2 as a dashed line and shade below the line.

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 (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it satisfies the inequality when substituted into it.

Front

How do you determine if a point (x, y) is a solution to the inequality y ≤ 5x - 1?

Back

Substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

What is a system of inequalities?

Back

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

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What does the inequality y ≥ -2x + 1 represent graphically?

Back

It represents a solid line with a slope of -2 and a y-intercept of 1, shaded above the line.