Question

find the equation of a line passing through the point(2,3) and inyersecting the line 2x-3y=6 on the y-axis?
[ hint :2x-3y=6 meets y -axis at (0,-2), so the required line passes through (0,-2)]

Answer 1

The given equation of the line is :$2x-3y=6$

Put $x=0$in the above equation, we get

$0-3y=6\Rightarrow y=-2$

So, the line $2x-3y=6$ intersect y-axis at $(0,-2)$

Now, the required line passes through points $(2,3)$and $(0,-2)$.

We know that equation of a line segment passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\frac{(y-y_1)}{(x-x_1)}$ = $\frac{(y_2-y_1)}{(x_2-x_1)}$

So, the equation of the required line that passes through points 2,3 and 0,-2 is

$\Rightarrow \frac{y-3}{x-2}=\frac{-2-3}{0-2}$

$\Rightarrow \frac{y-3}{x-2}=\frac{5}{2}$

$\Rightarrow 2y-6=5x-10$

$\Rightarrow 2y-5x+4=0$