Question

Find the equation of a line passing through the point $(3,-1)$ and making an intercept of $-4$ on $Y-axis$

Answer 1

Finding the equation of the line using slope intercept form.

Given that the line passes through the point $(3,-1)$ and has the $yintercept,c=-4$

The general equation of a line with slope $m$and $y-intercept$ as $c$ is given by

$y=mx+c$

$\Rightarrow y=mx-4$ ……………(1)

Now the point $(3,-1)$ lies on the line $y=mx-4$,

Thus, by putting, $x=3$ and $y=-1$ in $y=mx-4$, and solving for $m$, we get

$y=mx-4$

$\Rightarrow -1=3m-4$

$\Rightarrow 3m=3$

$\Rightarrow m=1$

Thus, the equation of the required line using equation (1) will be

$y=mx-4$

$\Rightarrow y=x-4$

Hence, the required equation of the line is given by $y=x-4$