Graphing Linear Inequalities Flashcard

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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality. Points in this region satisfy the inequality.

Front

What is the significance of a solid line in graphing linear inequalities?

Back

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

Front

What does a dotted line indicate in graphing linear inequalities?

Back

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

Front

How do you determine if a point is a solution to a linear inequality?

Back

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

Front

What is the slope of a line?

Back

Front

How do you graph the inequality y < mx + b?

Back

Graph the line y = mx + b with a dotted line, then shade below the line to represent all points where y is less than mx + b.

Front

What does the inequality y ≥ mx + b represent?

Back

It represents all points on or above the line y = mx + b, including the line itself.

Front

What is the solution set of the inequality 2x + 3 < y?

Back

The solution set includes all points above the line y = 2x + 3, not including the line itself.

Front

How do you identify the boundary line of a linear inequality?

Back

The boundary line is found by replacing the inequality sign with an equal sign and graphing the resulting equation.