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 that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

How do you graph a linear inequality in two variables?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or >, and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

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 which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (usually (0,0) if it's not on the line) to see if it satisfies the inequality. If it does, shade that side; if not, shade the opposite side.

Front

What does the inequality y > 2 represent on a graph?

Back

It represents all points above the horizontal line y = 2, not including the line itself.

Front

What does the inequality y ≤ -3/4x + 3 represent?

Back

It represents all points on or below the line y = -3/4x + 3, including the line itself.

Front

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

Back

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

Front

How can you express the solution to a linear inequality in interval notation?

Back

For x < -1, the interval notation is (-∞, -1). For y ≥ -3/4x + 3, it would depend on the specific x-values.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set and indicates where the inequality changes from true to false.