Question

If a straight line with slope $3$ intersects a straight line with slope $6$ at the point $(30,40)$. Then, the difference between the $y$-intercepts of the straight lines is

• A. $60$
• B. $70$
• C. $80$
• D. $90$
• E. $100$

Answer 1

The correct option is D $90$

Equation of straight line with slope $3$ and passing through the point $(30,40)$ is
$(y-40)=3(x-30)$
$\Rightarrow y-40=3x-90$
$\Rightarrow 3x-y=50$
$\Rightarrow \frac{x}{\left(\frac{50}{3}\right)}+\frac{y}{(-50)}=1$ .... (i)
And equation of straight line with slope $6$ and passing through the point $(30,40)$ is
$(y-40)=6(x-30)$
$\Rightarrow y-40=6x-180$
$\Rightarrow 6x-y=140$
$\Rightarrow \frac{x}{\left(\frac{70}{3}\right)}+\frac{y}{(-140)}=1$ .... (ii)
Therefore, the difference between the $y$-intercepts of the straight lines $=-50-(-140)=140-50=90$.