Write the equation of the line going through the point (4,6) that is perpendicular to the lie 3x+6y=12

3x + 6y = 12
6y = - 3x + 12
y = - 1/2x + 2

Since your slope is - 1/2, we take the opposite reciprocal to find the perpendicular slope. Your perpendicular slope is 2. 

y = 2x + b

Plug in the point to solve for b and get your final line. 

6 = 2(4) + b
6 = 8 + b
6 - 8 = b
- 2 = b

y = 2x - 2 is your perpendicular line

Can you provide the tape diagram?

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