$\begin {array} {1 1} (A)\;y + 2 = x + 1 & \quad (B)\;y+2=3(x+1) \\ (C)\;y - 2 = 3 (x - 1) & \quad (D)\;y-2=x-1 \end {array}$

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- Equation of a line having slope m and passing through $(x_1,y_1)$ is $ y-y_1=m(x-x_1)$
- If two lines are parallel then their slopes are equal.

Step 1 :

Equation of the given line is $y=3x-1$ or $3x-y-1=0$

Hence the slope of this line is $ - \bigg( \large\frac{3}{-1} \bigg)$ = 3

It is said that the required line passes through the point (1,2) and is parallel to the above line.

Hence the slope of this line is $m=3$

Step 2 :

Hence the equation of the required line is $y-y_1=m(x-x_1)$

$y-2=3(x-1)$

$ \Rightarrow y-2=3x-3$

or $ 3x-y=1$

Hence the correct option is 'C'

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