Question

Find the equation of a straight line:
with slope $-2$ and intersecting the $x-axis$ at a distance of $3$ units to the left of origin.

Answer 1

Let line $AB$ intersect the X-axis at a distance 3 units to the left of origin.

At X-axis, $y=0$

$\therefore$ Line AB cuts X-axis at $P(-3,0)$

& slope of the line $AB=-2$, i.e $m=-2$

We know that ,

Equation of line passing through $(x_0,y_0)$ with slope $m$is $y-y_0=m(x-x_0)$

Here, $x_0=3,y_0=0$

$m=-2$

Putting values, we get

$y-0=-2(x+3)$

$\Rightarrow y=-(2x+3)$

$\Rightarrow y=-2x-6$

$2x+y+6=0$

Hence, the required equation is $2x+y+6=0$