Describe the graph of 2x - 3y > 18, including intercepts, line style, and shading.

Step-by-step explanation:

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The graph of 2x - 3y > 18 is a dotted line passing through the intercepts (9, 0) and (0, -6).

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given inequality is 2x - 3y > 18.

Since the inequality sign does not include =, the line will be dotted.

Since the equation is linear, graph will be a line.

Consider 2x - 3y = 18

When x = 0, -3y = 18 or y = -6

y intercept is -6.

When y = 0, 2x = 18 0r x = 9

x intercept is 9.

The line touches the X axis at (9, 0) and the Y axis at (0, -6).

At origin (0, 0), the inequality 0 > 18 is not true.

Hence the shading of the graph will be below the line where the point origin is not included.

Hence the graph is given below.

Learn more about Linear inequalities here :

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