Question

Explain how to find the inequality that represents the graph.

Answer 1

The inequality that represents the given graph is y < x/5 -2 OR 5y < x - 10

Graph of Inequality

From the question, we are to determine the inequality that represents the graph

First, we will assume the inequality is a straight line and we will determine the equation of the line

From the graph, we have two points on the line

(0, -2) and (5, -1)

Using the formula for the equation of a line with two given point

(y - y₁)/(x -x₁) = (y₂ - y₁)/ (x₂ - x₁)

x₁ = 0

y₁ = -2

x₂ = 5

y₂ = -1

Thus,

(y - -2)/(x - 0) = (-1 - -2)/ (5 - 0)

(y +2)/(x - 0) = (-1 + 2)/ (5 - 0)

(y +2)/(x ) = 1/ 5

5(y + 2) =1(x)

5y + 10 = x

5y = x - 10

y = 1/5(x) - 2

y = x/5 - 2

Now,

Since the solution is below the line and the line is dotted

The inequality becomes

y < x/5 -2

OR

5y < x - 10

Hence, the inequality that represents the given graph is y < x/5 -2 OR 5y < x - 10

Learn more on Graph of Inequality here: brainly.com/question/17106134

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