Originally Posted by

**ukorov** ...

*3. Parallel to 3x-4y=2 passing through (1, 2)*

**I did: 3x-4y =3 x 1 - 4 x 1**

**=3x-4y=-1**

What you presented is wrong. (1,2) lies on a line that is parallel to another line 3x - 4y = 2. it does not mean (1,2) simply lies on this 3x - 4y = 2.

Being parallel means the two lines share the same slope, m.

3x - 4y = 2

3x - 2 = 4y

y = $\displaystyle \frac{3}{4}x - \frac{1}{2}$

hence its slope = $\displaystyle \frac{3}{4}$

Therefore, the equation of the line parallel to 3x - 4y = 2 and passes through (1,2) is:

$\displaystyle \frac{y - 2}{x - 1} = \frac{3}{4}$

In the end you get 7x - 4y + 1 = 0

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