Graphing Linear Inequality

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 in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the values of the variable can be less than or equal to the value on the other side of the inequality.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable can be greater than or equal to the value on the other side of the inequality.

Front

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

Back

The slope in a linear inequality indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means that as one variable increases, the other also increases.

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0) if it's not on the line). Substitute the coordinates of the test point into the inequality. If the inequality holds true, shade the side containing the test point.

Front

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

Back

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

Front

How can you convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form (y = mx + b), isolate y on one side of the inequality. This allows you to easily identify the slope (m) and y-intercept (b).

Front

What is the y-intercept of the inequality y ≤ -3/5x + 3?

Back

The y-intercept of the inequality y ≤ -3/5x + 3 is 3, which is the point where the line crosses the y-axis.

Front

What does the inequality y > 1 represent graphically?

Back

The inequality y > 1 represents all points above the horizontal line y = 1, not including the line itself.