Two- Variable Inequalities

Front

What is a two-variable inequality?

Back

Front

How do you graph a two-variable inequality?

Back

To graph a two-variable inequality, 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 shaded region in a graph of a two-variable inequality represent?

Back

The shaded region represents all the possible solutions (x, y) that satisfy 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 in a two-variable inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Front

What is the standard form of a linear inequality?

Back

Front

Back

Front

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

Back

Front

How do you convert a linear equation to an inequality?

Back

To convert a linear equation to an inequality, replace the equality sign (=) with an inequality sign (<, >, ≤, or ≥) based on the context of the problem.

Front

What is the significance of the y-intercept in a graph of a linear inequality?

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.