First we need to arrange the given equation into slope-intercept form, as follows:
2x + 12y = -1
Subtracting 2x from both sides, we get:
12y = -2x -1 ................(1)
Next we divide both sides of equation (1) by 12, to get:
\(y=-\frac{1}{6} x-\frac{1}{12} ...........(2)\)
Therefore the slope in equation (2) is -(1/6)
The product of the slope of the perpendicular line and the slope of the given equation must equal -1. Let the slope of the perpendicular line be m. Then we can write:
\(m\times -\frac{1}{6}=-1 ............(3)\)
Multiplying both sides of equation (3) by -6, results in:
m = 6
So the required number to type in the box is 6.
