Algebra 1 - 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

How do you graph an inequality in two variables?

Back

To graph an inequality in two variables, first graph the corresponding equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the region that satisfies the inequality.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that make the inequality true.

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 difference between a solid line and a dashed line when graphing inequalities?

Back

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

Front

What does the graph of y ≤ 2/5x + 1 look like?

Back

The graph of y ≤ 2/5x + 1 is a shaded region below the line y = 2/5x + 1, including the line itself.

Front

How do you identify the correct graph for a given inequality?

Back

To identify the correct graph for a given inequality, look for the line that corresponds to the equation and check the shaded region to see if it matches 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.