Question 1076487
(2/3)x+y=16
kx+3y=48
if kx=2, then 2x+3y=48 and multiplying the top by 3, 2x+3y=48, the same.
Therefore k=2 for infinite solutions.
The slope of the first is -2/3, and slope intercept form is -2x/3+16
the slope of the second is -(1/3)k and slope intercept form is -k/3+16
For k equal to any other number than 2, there will be one point of intersection.  
For no solution, the two lines have to be parallel, and the line kx+3y=48 becomes 3y=-kx+48 and 
y=-(k/3)+16.  The y-intercept doesn't change with k, so there is no value where the lines are parallel without being the same line.