Question

Find the equation of a line passing through the point $(2,3)$and parallel to the line $3x-4y+5=0$

• A. $4x-3y+6=0$
• B. $3x-4y+6=0$
• C. $3x+3y-6=0$
• D. None of these

Answer 1

The correct option is B

$3x-4y+6=0$

Find the equation of a line passing through the given point

The given equation of the line is $3x-4y+5$

The equation of line parallel to $3x–4y+5=0$ is $3x–4y+c=0$

$\because$Line passes through the point $(2,3)$ so it is the solution of line

Substitute the values $x=2$ and $y=3$ in the equation $3x-4y+c$

$$\begin{gathered} \Rightarrow 3\left(2\right)–4\left(3\right)+c=0 \\ \Rightarrow 6–12+c=0 \\ \Rightarrow -6+c=0 \\ \Rightarrow c=6 \end{gathered}$$

So the required equation of line is $3x–4y+6=0$

Hence the correct option is option (B) i.e $3x-4y+6=0$