5-6 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 (like <, >, ≤, or ≥) 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 to that 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 (≤ 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 an inequality?

Back

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

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

How do you graph the inequality y < -4x - 1?

Back

To graph y < -4x - 1, first graph the line y = -4x - 1 as a dashed line. Then shade the region below the line to represent all the points where y is less than -4x - 1.

Front

What does the inequality 3x + 2y ≤ 24 represent in a real-world context?

Back

The inequality 3x + 2y ≤ 24 represents a budget constraint where x is the number of apples and y is the number of oranges, and the total cost cannot exceed $24.

Front

How can you express a real-world situation as an inequality?

Back

To express a real-world situation as an inequality, identify the quantities involved, determine the relationship between them, and use appropriate inequality symbols to represent constraints.

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. It helps in plotting the line for the inequality and understanding the relationship between the variables.

Front

What does the inequality y ≥ 3/4x + 5 indicate about the graph?

Back

The inequality y ≥ 3/4x + 5 indicates that the graph includes the line y = 3/4x + 5 (solid line) and the region above the line, where y values are greater than or equal to the line.