Question

The equation of the line passing through $(2,-1)$ and parallel to $3x+4y=10$ is

• A. $3x+4y+2=0$
• B. $3x-4y-2=0$
• C. $3x+4y-2=0$
• D. $3x-4y+2=0$

Answer 1

The correct option is C $3x+4y-2=0$

The equation of a line parallel to another line $ax+by=c$......(i) is $ax+by=k$.......(ii)

If the line (ii) passes through a point $P(p,q)$, then $k$ can be evaluated by putting $x=p$ and $y=q$ in (ii).
Given the equation of line:
$3x+4y=10$
A line parallel to the given line be: $3x+4y=k$
This line passes through $(2,-1)$
Thus, $3\left(2\right)+4(-1)=k$
$\Rightarrow k=6-4$
$\Rightarrow k=2$
Hence, the required line is: $3x+4y=2$.