Graphing systems of inequalities!

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are graphed on the same coordinate plane.

Front

How do you graph the inequality y > -1/5x - 1/2?

Back

Shade the region above the line y = -1/5x - 1/2, which is dashed because the inequality is strict (greater than).

Front

What does it mean when the graph of y ≥ x - 3 is shaded above?

Back

It indicates that all points above the line y = x - 3, including the line itself, are solutions to the inequality.

Front

How do you determine where to shade for the inequality y < -2x - 4?

Back

Shade the region below the line y = -2x - 4, which is dashed because the inequality is strict (less than).

Front

What is the solution set for the system of inequalities y > -1/5x - 1/2 and y ≤ -2x - 4?

Back

The solution set includes all points that satisfy both inequalities, represented by the overlapping shaded regions.

Front

What does the inequality x > 2 represent on a graph?

Back

It represents all points to the right of the vertical line x = 2, not including the line itself.

Front

Which of the following points is NOT a solution to the system of inequalities: y > -1/5x - 1/2 and y ≤ -2x - 4? (0,-1), (0,3), (4,0), (6,-2)

Back

(0,-1) is NOT a solution because it does not satisfy both inequalities.

Front

What does it mean if a line is dashed in a graph of inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (strict inequalities).

Front

What does the inequality y ≥ -2x - 4 indicate about the graph?

Back

It indicates that the region above the line y = -2x - 4, including the line itself, is part of the solution set.

Front

How do you identify the boundary line for the inequality y < -1/5x - 1/2?

Back

The boundary line is found by replacing the inequality with an equal sign: y = -1/5x - 1/2.