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 (such as <, >, ≤, 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 possible solutions to that inequality, showing the region of the coordinate plane 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 set (≤ 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 does the solution set of an inequality look like on a graph?

Back

The solution set of an inequality is represented by a shaded region on the graph, indicating all the points that satisfy the inequality.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph the inequality y < mx + b?

Back

To graph y < mx + b, first graph the line y = mx + b using a dashed line, then shade the region below the line to represent all points where y is less than mx + b.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, and it helps to determine the starting point for graphing the inequality.

Front

What does it mean for a point to be 'not part of the solution set'?

Back

A point is 'not part of the solution set' if it does not satisfy the inequality when its coordinates are substituted into the inequality.

Front

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

Back

To determine which side of the line to shade, you can test a point not on the line (like (0,0) if it's not on the line) in the inequality. If the inequality is true, shade that side; if false, shade the opposite side.