Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

What type of line is used to represent the inequality y ≥ x + 1 on a graph?

Back

A solid line is used to represent the inequality y ≥ x + 1 because the inequality includes 'greater than or equal to'.

Front

What type of line is used to represent the inequality y < x - 1 on a graph?

Back

A dotted line is used to represent the inequality y < x - 1 because the inequality does not include 'less than or equal to'.

Front

How do you graph the inequality y ≤ 2/5x + 1?

Back

1. Graph the line y = 2/5x + 1 using a solid line. 2. Shade below the line to indicate all the points where y is less than or equal to the line.

Front

What is the solution set of the inequality y > -2x?

Back

The solution set includes all points above the line y = -2x, not including the line itself.

Front

What does it mean if a point (x, y) satisfies the inequality y < 3x + 2?

Back

It means that when you substitute x into the equation 3x + 2, the value of y must be less than the result.

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between 'y < x' and 'y ≤ x'?

Back

'y < x' means y is strictly less than x (not including x), while 'y ≤ x' means y can be less than or equal to x (including x).