Question 250706
First of all rearrange 3x+4y-8 = 0 into the form y=mx+c

4y = -3x+8
y = -3/4x + 2

Since we know that the second line is parallel to y = -3/4x + 2 then the gradient must be the same. The gradient is -3/4.

So we know that the second line is y=-3/4x + c . To find c we need to plug in the values of the point (2,3). 3 = -3/2 + c 

Rearrange to find c = 3 + 3/2 = 9/2

So the equation is y = -3/4x + 9/2

If we plot the two lines we can see that they are parallel

{{{ graph( 300, 300, -5, 5, -5, 5, (-3/4)*x-2, (-3/4)*x + 9/2) }}}