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

How do you determine if the shading is above or below the line in a linear inequality?

Back

If the inequality is of the form y > mx + b or y ≥ mx + b, shade above the line. If it is y < mx + b or y ≤ mx + b, shade below the line.

Front

What does a dashed line represent in graphing linear inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict: > or <).

Front

What does a solid line represent in graphing linear inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict: ≥ or ≤).

Front

How do you graph the inequality x + 3y > 6?

Back

First, graph the line x + 3y = 6 as a dashed line. Then, shade the region above the line.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you convert the inequality 3x - y > 4 into slope-intercept form?

Back

Rearranging gives y < 3x - 4, which is in slope-intercept form.

Front

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

Back

A point is a solution if it satisfies the inequality and lies in the shaded region of the graph.

Front

Is the point (3, 1) a solution for the inequality y < 3x - 4?

Back

No, because when substituting (3, 1) into the inequality, it does not satisfy the condition.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as either a dashed or solid line.