Question

The equation of the line passing through point $P(-3,7)$ and having slope $m=\frac{1}{2}$ is

• A. $x+2y+17=0$
• B. $x-2y+17=0$
• C. $2y-x+17=0$
• D. $2y-x-17=0$

Answer 1

The correct option is B $x-2y+17=0$

Let us take the line in slope-intercept form, which is $y=mx+c$ ........... $\left(i\right)$

It passes through the point $P(-3,7)$ and slope $m=\frac{1}{2}$

If a line passes through point $P(p,q)$ and slope $m=a$, then the value of $c$ can be obtained by putting

$x=p,y=q$ and $m=a$

Here, $p=-3,q=7$ and $m=\frac{1}{2}$

Substituting $x=p=-3,y=q=7$ and $m=a=\frac{1}{2}$ in $\left(i\right)$ we get

$7=\frac{1}{2}\times (-3)+c⟹c=\frac{17}{2}$

$\therefore \left(i\right)$ becomes $y=\frac{1}{2}x+\frac{17}{2}⟹x-2y+17=0$

Hence, option B is correct.