Graph two-variable inequality

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 \leq or \geq. Finally, shade the region that satisfies the inequality.

Front

What does the shaded area in a graph of a two-variable inequality represent?

Back

The shaded area 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 (\geq or \leq), while a dashed line indicates that points on the line are not included ( > or < ).

Front

Back

It represents all points above and including the horizontal line at y = -1.

Front

How do you determine if a point is a solution to a two-variable inequality?

Back

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

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Back

The solution set includes all values of x that are greater than 2, represented graphically as a dashed vertical line at x = 2 with shading to the right.

Front

Back

It indicates that the solution includes all points below the horizontal line at y = -3, not including the line itself.

Front

What is the significance of the boundary line in a two-variable inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

How can you check if a point lies in the solution region of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality is true, the point lies in the solution region.