Question

Write the following inequality in slope intercept form -12x - 2y is greater than or equal to -42

Answer 1

First of all, we write the requested inequality:

`-12x-2y\geq -42`

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

`-2y\geq 12x-42`

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

`y \leq -6x+21`

Answer 2

y ≤ -6x + 21 is the inequality.

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

`((-12x-2y))/(2)\geq  (-42)/(2)`

-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