Question

Find the equation of the line through the intersection of $3x+4y-7=0$ and $x=y-2$, and slope $5$.

• A. $35x-7y+18=0$
• B. $33x-7y+18=0$
• C. $35x-8y+18=0$
• D. $35x-7y+20=0$

Answer 1

Answer: (A)

Given lines are $3x+4y-7=0$ and $x-y+2=0$
Any line through the intersection of these lines is
$3x+4y-7+k\left(x-y+2\right)=0\dots \left(i\right)$
which can be written as
$\left(3+k\right)x+\left(4-k\right)y-7+2k=0$
Slope of this line $=-\left(\frac{3+k}{4-k}\right)$
$\therefore$ We must have $-\left(\frac{3+k}{4-k}\right)=5$
$\Rightarrow -3-k=20-5k$
$\Rightarrow 4k=23$
$\Rightarrow k=\frac{23}{4}$.
Substituting this value of $k$ in $\left(i\right)$, we get
$3x+4y-7+\frac{23}{4}\left(x-y+2\right)=0$
$\Rightarrow 35x-7y+18=0$