Question

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

Answer 1

-12x-2y≤-42 add 12x to both sides

-2y≤12x-42 divide both sides by -2 (and reverse direction of inequality because of division by a negative)

y≥-6x+21

Answer 2

The inequality in slope-intercept form is given by:

`y\geq -6x+21`

Explanation:

We know that a equation in the slope-intercept form is given by:

`y=mx+c`

where m is the slope and c is the y-intercept form of the line.

Now, if we have to write the inequality in slope-intercept form then the equality sign is replaced by the inequality sign.

Here we have the inequality as follows:

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

Now, we add 12x on both the side of the inequality to obtain:

`-2y\leq -42+12x`

Now, we multiply both side of the inequality by -1 to get:

`2y\geq -(-42+12x)\\\\i.e.\\\\2y\geq 42-12x\\\\i.e.\\\\2y\geq -12x+42`

Now, we divide both side of the inequality by 2 to obtain:

`y\geq -6x+21`