Question

Equation of the line passing through $(1,2)$ and parallel to the line $y=3x-1$ is

• A. $y+2=x+1$
• B. $y+2=3(x+1)$
• C. $y–2=3(x–1)$
• D. $y–2=x–1$

Answer 1

The correct option is C

$y–2=3(x–1)$

Step 1. Find the slope of the given equation:

equation of the line is $y=3x–1$

and points are $(1,2)$

$\because$The given equation is in $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathit{m}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathit{b}$ the form

$\Rightarrow$ $m=3$

Thus the slope of the required line would be $m=3$

As The line parallel to the line $y=3x-1$

Step 2. Find the required equation of line:

$\because y–y_1=m(x–x_1)$

$\Rightarrow$$\mathit{y}\mathbf{}\mathbf{–}\mathbf{}\mathbf{2}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{(}\mathit{x}\mathbf{}\mathbf{–}\mathbf{}\mathbf{1}\mathbf{)}$

Hence, Option ‘C’ is Correct.