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, typically shown as a shaded region on one side of a boundary line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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

Front

What does the inequality y ≥ -3/4 x + 3 mean?

Back

It means that the y-values are greater than or equal to the values on the line defined by the equation y = -3/4 x + 3.

Front

How do you graph the inequality y < 2x - 1?

Back

First, graph the line y = 2x - 1 with a dashed line, then shade below the line to represent all y-values less than the line.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).

Front

How can you tell which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (like (0,0)) in the inequality. If the inequality is true, shade the side containing that point.

Front

What is the solution set of the inequality y < 3?

Back

The solution set includes all points below the horizontal line y = 3.