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andrey2020 [161]
2 years ago
7

Find a linear inequality with the following solution set. Each grid line represents one unit.

Mathematics
1 answer:
alukav5142 [94]2 years ago
4 0

The <em>linear</em> inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

<h3>How to derive the inequality that represents the image</h3>

Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a <em>linear</em> function, that is, a <em>first grade</em> polynomial. By geometry we know that a equation of the line can be known from two distinct points set on <em>Cartesian</em> plane:

Slope

m = [- 4 - (- 2)] / [4 - (- 2)]

m = (- 2) / 6

m = - 1 / 3

Intercept (m = - 1 / 3, (x, y) = (4, - 4)

b = y - m · x

b = - 4 - (- 1 / 3) · 4

b = - 4 + 4 / 3

b = - 8 / 3

Then, we find that the inequality is:

y ≤ (- 1 / 3) · x - 8 / 3

8 / 3 ≤ (- 1 / 3) · x - y

(- 1 / 3) · x - y ≥ 8 / 3

The <em>linear</em> inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.

To learn more on inequalities: brainly.com/question/17675534

#SPJ1

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