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 ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). 2. Choose a test point not on the line to determine which side of the line to shade. 3. Shade the region that satisfies the inequality.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to the value on the other side of the inequality.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to the value on the other side of the inequality.

Front

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

Back

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

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, you can use a test point (often (0,0) if it is not on the line). Substitute the coordinates of the test point into the inequality. If the inequality holds true, shade the side of the line that includes the test point.

Front

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

Back

Front

How do you convert a linear inequality to slope-intercept form?

Back

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. It helps in graphing the inequality and indicates the starting point of the line on the y-axis.

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 means that the point satisfies the corresponding linear equation. Whether it is included in the solution set depends on whether the inequality is strict (< or >) or non-strict (≤ or ≥).