Question

Write the coordinates as an ordered pair for any point that is a solution to the of inequality graphed below.

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Answer 1

The inequality that represents the graph must have the following form:

`y > -4\cdot x + 6`

Explanation:

First, we need to determine the equation of the line which represents the "lower" bound of the inequality:

`y = m\cdot x + b` (1)

Where:

`x` - Independent variable, horizontal axis.

`y` - Dependent variable, vertical axis.

`m` - Slope.

`b` - Intercept.

Given two distinct points of the line, we can solve for both slope and intercept:
`(x_(1), y_(1)) = (1, 2)`,
`(x_(2), y_(2)) = (0, 6)`

`m + b = 2` (2)

`b = 6` (3)

The solution of the system is:
`m = -4`,
`b = 6`

Then, the inequation must have the following form:

`y > -4\cdot x + 6`