The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
How to derive the inequality that represents the image
Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian 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 linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
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