Question

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

Answer: (D)

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