what is the parallel to 2x-3y=4 passing through (2,6)

Question

marigirl · Answer

first i am going to rewrite the equation in the form y=mx+c
2x-3y=4
   -3y=4-2x
      y=-4/3+2/3x
$$y=\frac{ 2 }{ 3 }x-\frac{ 4 }{ 3 }$$

marigirl · Answer

from this we can see that the gradient of that equation is m=2/3

marigirl · Answer

If this new line is parallel to this equation then it will have the same gradient.. therefore m=2/3 .. and from the question we have a given coordinate (2,6)

marigirl · Answer

what we can do now is use this information to obtain that new equation
y-y1=m(x-x1)
y-6 =(2/3)(x-2) 
expand
$$y-6=\frac{ 2 }{ 3 }x-\frac{ 4 }{ 3 }$$
then add 6 t bth sides
$$y=\frac{ 2 }{ 3 }x-\frac{ 22 }{ 3 }$$

anonymous · Answer

Marigirl, many thanks for your help.

marigirl · Answer

no prbs! can u plz give me a medal