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# Choose the correct answer from the given four options.Equation of the line passing through (1, 2) and parallel to the line y = 3x-1 is

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

Toolbox:
• 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'