Graphing Inequalities

Front

What does the inequality y ≥ -3 represent on a graph?

Back

The region above the horizontal line y = -3, including the line itself.

Front

What is the difference between y > 2 and y ≥ 2?

Back

y > 2 means the line is dashed and does not include the line y = 2; y ≥ 2 includes the line y = 2 and the area above it.

Front

How do you graph the inequality y < x + 1?

Back

Draw a dashed line for y = x + 1 and shade below the line.

Front

What does the inequality y ≤ -x + 1 indicate?

Back

The region below the line y = -x + 1, including the line itself.

Front

What is the solution set for the inequality y > x + 1?

Back

The area above the line y = x + 1, not including the line.

Front

How do you determine if a point (2, 3) is a solution to the inequality y < 2x - 5?

Back

Substitute x = 2 into the inequality: 3 < 2(2) - 5, which simplifies to 3 < -1 (false). So, (2, 3) is not a solution.

Front

What does the inequality x ≥ -5 represent on a number line?

Back

All numbers to the right of -5, including -5 itself.

Front

How do you graph the inequality y ≥ 2x - 5?

Back

Draw a solid line for y = 2x - 5 and shade above the line.

Front

What is the meaning of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set.

Front

What does the inequality y < 2 indicate on a graph?

Back

The region below the horizontal line y = 2, not including the line.