Question

find the equation of line passing through the point 1, 4 and intersecting the line x minus 2 Y - 11 is equal to zero on y axis

Answer 1

equation 1 is ? 
equation 2 is x-2y-11=0

the coordinates of the intersecting point belongs to both equations.
At y-axis,x=0. Putting it in eq 2,
0-2y-11=0
-2y=11
y= -11/2

So intersecting coordinate is (0, -11/2)

gradient(m)= (y1-y2)/(x1-x2)
={(-11/2)-4}/(0-1)
=19/2

Now put the values in the equation of straight line which is,
y-y1=m(x-x1),,,,, y1,x1 are coordinates on eq 1, m is the gradient of eq 1
y-4=(19/2)(x-1)
2y-8=19x-19
2y=19x-19+8
2y=19x-11 (ans)