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.
