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 (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, showing the region of the coordinate plane that satisfies the inequality.

Front

How do 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 coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

To convert a linear inequality to slope-intercept form, isolate y on one side of the inequality.

Front

What does a dashed line represent in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line represent in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

What is the significance of the shading in the graph of a linear inequality?

Back

The shading indicates the region of the graph that contains all the solutions to the inequality.

Front

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

Back

Graph the line y = 2x + 3 with a dashed line, then shade above the line to represent y values greater than the line.

Front

What is the solution set of the inequality x < -1?

Back

The solution set includes all real numbers less than -1, represented by the shaded region to the left of -1 on the number line.