Question

find the equation of the line passing through the point (1,4) and intersecting the line
$x - 2y - 11 = 0$
on the y axis

THE FIRST ONE TO ANSWER WILL BE MARKED AS BRIANLIEST

Answer 1

Given that point of intersection of lines  x - 2y - 11 = 0 is (1,4).

Given that it lies on the y-axis.Then the x-axis will be 0.

Substitute x = 0 in the above equation, we get

0 - 2y - 11 = 0

-2y - 11 = 0

2y + 11 = 0

2y = -11

y = -11/2.


Hence the point of the y-axis is(0,-11/2).

Now,

The equation of the line passing through points is:

$\frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1}$

$\frac{y - 4}{x - 1} = \frac{ \frac{-11}{2} - 4}{0 - 1}$

$\frac{y - 4}{x - 1} = \frac{2 * 4 + 11}{2}$

$\frac{y - 4}{x - 1} = \frac{19}{2}$

2y - 8 = 19x - 19

2y = 19x - 19 + 8

2y = 19x - 11

19x - 2y - 11 = 0



Therefore the equation of the line is 19x - 2y - 11 = 0.



Hope this helps!