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6

Step-by-step explanation:

Slope intercept form is y = mx + b

Step 1: Isolate y

To convert to slope - intercept form, we first want the term with y, on one side of the equation, and all the other terms on the other side. Since 2x is being added to 12y, we can subtract 2x from both sides.

2x + 12y = -192

12y + 2x = -192

12y = -192 - 2x

We also want to have the x term before any other terms in slope - intercept form. So we can simply move the x term to the left because both operations are the same (subtraction and subtraction)

12y = -192 - 2x

12y = -2x - 192

Step 2: Remove all terms with y

Now we just want y alone on one side of the equation. For this, we can divide all sides by 12 to isolate y, because y is being multiplied by 12. (opposite operation of multiplication is division)

12y = -2x - 192

12(y) = -2x - 192

y = (-2 - 192)/12

y = -1/6x - 16

Now we have our slope - intercept form equation ready.

The perpendicular slope of a line is the opposite reciprocal of the slope of that line. This means that you find the opposite operation( subtraction and addition) of the slope, and the reciprocal (flip the numerator and denominator).

With this in mind, we can do that to our slope of -1/6

Step 1: Find the opposite

Easy, we are subtracting 1/6, so we can turn it into addition

-1/6   1/6

Step 2: Find the Reciprocal

This is also easy, just flip the numbers in the numerator and the denominator

1/6   6/1   6

The slope of the line perpendicular to 2x + 12y = -192 is 6

-Chetan K