Question

Which of the following inequalities matches the graph?

graph of an inequality with a solid horizontal line through the origin and shading below the line.
x less than or greater to 0
x greater than or equal to 0
y less than or greater to 0
y greater than or equal to 0

Answer 1

y less than or equal to 0

Explanation:

We are given that,

The graph of the inequality is the 'horizontal line passing through the origin and is shaded below the line'.

Since the 'horizontal line passing through the origin' is represented by the x-axis.

We get that, the graph is shaded below the x-axis.

So, the graph of the inequality is given by the set y i.e. 'y less than or equal to 0'.

Answer 2

The correct answer is:

y less than or equal to 0 , or y ≤ 0.

Explanation:

The line drawn tells us what the equation will be that the inequality is formed from. Since the line is a horizontal line, this means it is of the form y=c, where c is some constant.

Since the horizontal line goes through the origin, (0, 0), this means the equation of the line is y=0.

Since the line drawn is solid, this means the inequality symbol will be either greater than or equal to, or less than or equal to. This is because the line is included in the solution set.

Since the graph is shaded below this line, this means our inequality is

y ≤ 0, or

y is less than or equal to 0.