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 it mean to graph a linear inequality?

Back

Graphing a linear inequality involves drawing the boundary line of the inequality and shading the appropriate region to represent all solutions.

Front

How do you determine if you need to flip the inequality sign?

Back

You need to flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

What is the significance of the boundary line in graphing linear inequalities?

Back

The boundary line represents the values where the inequality changes from true to false. If the inequality is strict (>, <), the line is dashed; if it is inclusive (≥, ≤), the line is solid.

Front

How do you find the y-intercept of a linear inequality?

Back

To find the y-intercept, set x = 0 in the inequality and solve for y.

Front

What does shading above the line indicate in a graph of a linear inequality?

Back

Shading above the line indicates that the solutions to the inequality are greater than the values on the line.

Front

What does shading below the line indicate in a graph of a linear inequality?

Back

Shading below the line indicates that the solutions to the inequality are less than the values on the line.

Front

How can you convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form (y = mx + b), isolate y on one side of the inequality.

Front

What is the slope-intercept form of the inequality 2x + 3y < 6?

Back

The slope-intercept form is y < -2/3x + 2.

Front

What is the first step in graphing the inequality 3x - y > 4?

Back

The first step is to rewrite the inequality in slope-intercept form.