we are given the following equation:
[tex]y=\frac{2}{3}x+4[/tex]An equation so that the system has an infinite solution is an equation that is equivalent to this equation, for example:
[tex]\begin{gathered} y=\frac{2}{3}x+4,(1) \\ 3y=2x+12,(2) \end{gathered}[/tex]In this case, equation (2) is equal to equation one multiplied by three.
For the system to have a solution the equations must have a different slope, for example:
[tex]\begin{gathered} y=\frac{2}{3}x+4,(1) \\ y=4x+4,(2) \end{gathered}[/tex]For the system to have no solutions, their slopes must be equal but not their y-intercept, for example:
[tex]\begin{gathered} y=\frac{2}{3}x+4,(1) \\ y=\frac{2}{3}x+5,(2) \end{gathered}[/tex]