Respuesta :

First of all, we write the requested inequality:

[tex]-12x-2y\geq -42[/tex]

The slope-intercept form of a line is [tex]y=mx+q[/tex], so we basically have to solve the inequality for y: we move the -12x term to the right:

[tex]-2y\geq 12x-42[/tex]

And we divide both sides by -2. Note that, since -2 is negative, this division also inverts the inequality sign:

[tex]y \leq -6x+21[/tex]

Answer:

y ≤ -6x + 21 is the inequality.

Step-by-step explanation:

A slope intercept form of a line is represented as y = mx + c

where m = slope of the line

and c = y intercept

The given inequality is -12x - 2y ≥ -42

Now we divide the inequality by 2

[tex]\frac{(-12x-2y)}{2}\geq  \frac{-42}{2}[/tex]

-6x - y ≥ -21

Now we add y on both the sides of the inequality

-6x - y + y ≥ -21 + y

-6x ≥ y - 21

We add 21 on both the sides of the inequality

-6x + 21 ≥ y - 21 + 21

-6x + 21 ≥ y

Or y ≤ -6x + 21

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