Verified Answer :

Step 1: Find the slope of 3x - 7y = 6

 3x - 7y = 6
- 3x        -3x
___________
-7y = -3x + 6
-------------------
          -7

y = 3/7 x - 7/6

So the slope from this equation is 3/7. Since the line is going to be perpendicular, this slope needs to be the opposite reciprocal. In order to do this, you need to flip 3/7 upside down and make it negative.

Step 2: Use point - slope form to find the y - intercept from the ordered pair
(0, -6/7).

Formula for point - slope form is y - y1 = m (x - x1)

      y - (-6/7) = -7/3 (x - 0)
      y + 6/7 = -7/3 (x - 0)
      y + 6/7 = -7/3x + 0
         -6/7             -6/7
----------------------------------
       y = -7/3x - 6/7

This step proves that the y - intercept has to be -6/7.

Step 3: Your final answer should be y = -7/3 - 6/7. 






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