Graphing Inequalities in Two Variables

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, showing the region of the coordinate plane where the inequality holds true.

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

Front

How do you graph the inequality y > 3/4x + 5?

Back

1. Graph the line y = 3/4x + 5 using a dashed line. 2. Shade the region above the line to represent y values greater than the line.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the ordered pairs (x, y) that satisfy the inequality.

Front

How can you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the significance of the y-intercept in graphing inequalities?

Back

The y-intercept is the point where the graph crosses the y-axis, and it helps in plotting the line for the inequality.

Front

What does the inequality y ≤ 3/4x + 5 indicate about the solution set?

Back

The inequality y ≤ 3/4x + 5 indicates that the solution set includes all points on the line and below it.

Front

How do you identify the boundary line of an inequality?

Back

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

Front

What is the role of the inequality symbol in determining the shading direction of the graph?

Back

The inequality symbol indicates whether to shade above or below the boundary line: > or ≥ means shade above, while < or ≤ means shade below.