Question

The equation of the line which passes through the point $(3,4)$, and whose y- intercept is twice its x-intercept, is

• A. $2x-y=0$
• B. $x+2y=10$
• C. $2x+y=10$
• D. none of these

Answer 1

The correct option is C $2x+y=10$

Equation of a line of slope ${}^{\prime }{m}^{\prime }$ which passes through joint $(3,4)\to y-4_1=m(x-x_1)$

$y-4=mx-3m\}$ equation of line -----$\left(1\right)$

Given, $y-$ intercept $=2(x-intercept)----\left(2\right)$

$y-$intercept = when $x=0$

$\therefore y-4=-3m$

$\Rightarrow y=4-3m$

$x-$ intercept is when $y=0$

$\therefore -4=mx-3m$

$\Rightarrow x=\frac{3m-4}{m}$

Using $\left(2\right)$

$4-3m=\frac{2(3m-4{)}^{-1}}{m}$

$\Rightarrow m=-2$

$\therefore$ equation of line $y-4=-2x+6\}$ from $\left(1\right)$

$\Rightarrow [2x+y=10]$