Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

Front

What does the symbol < indicate in a linear inequality?

Back

The symbol < indicates that the values of the variable are less than the value of the expression, and the line is dashed when graphed.

Front

What does the symbol ≤ indicate in a linear inequality?

Back

The symbol ≤ indicates that the values of the variable are less than or equal to the value of the expression, and the line is solid when graphed.

Front

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

Back

Shading indicates the set of solutions that satisfy the inequality; the shaded area represents all the points that make the inequality true.

Front

How do you determine which side of the line to shade for the inequality y < 2x + 3?

Back

To determine which side to shade, pick a test point not on the line (like (0,0)), substitute it into the inequality, and if the inequality holds true, shade that side.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Front

What does the graph of y > x + 3 look like?

Back

The graph of y > x + 3 is a dashed line with a slope of 1 and a y-intercept of 3, with shading above the line.

Front

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

Back

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

Front

How do you convert a linear equation to an inequality?

Back

To convert a linear equation to an inequality, replace the equals sign with an inequality symbol (<, >, ≤, or ≥) based on the context of the problem.