Passing through (2,7), parallel to 3x-6y=2?

Since the required line parallel to 3x - 6y = 2,
Let 3x - 6y = c be the equation of the required line.

Since the required line passes through (2, 7):
3(2) - 6(7) = c
c = -36

Equation of the required line:
3x - 6y = -36
x - 2y + 12 = 0

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Alternative method:

For the line 3x - 6y = 2,
slope = -3/(-6) = 1/2
Slope of the required line = 1/2

Equation of the required line:
y - 7 = (1/2)(x - 2)
2y - 14 = x - 2
x - 2y + 12 = 0

Same slope, thus is written as 3x - 6y = ?
Now, use the given point (2,7) to find the "?". 
Done!


What do you get?

The line is 3x - 6y = (some value)

Rearrange original to y = mx + b

3x - 6y = 2
-6y = -3x + 2

y = 1/2x - 1/3

Use y = 1/2x + b, Plug in your point

7 = (1/2)2 + b
6 = b

y = 1/2x + 6

Multiply by -6

-6y = -3x - 36

3x - 6y = -36