Answer :
An equation system has an infinite amount of solution when all the equations that conform it correspond to the same line.
The line shown in the graph has the equation y = 3x - 1
The equation that is equal to the graphed one will be the one that forms a system with an infinite number of solutions.
What you have to do is express each option in slope-intercept form and compare it to the given one:
1.
[tex]\begin{gathered} y+1-3x=0 \\ y+1-1+3x=-1 \\ y+3x-3x=-1-3x \\ y=-3x-1 \end{gathered}[/tex]This option does not form a system with infinite solutions with the given equation.
2.
[tex]y=-3x+1[/tex]This equation has a different slope and y-intercept than the given line, so it does not form a system with infinite solutions with it.
3.
[tex]\begin{gathered} y-3x+1=0 \\ y-3x+3x+1=3x \\ y+1-1=3x-1 \\ y=3x-1 \end{gathered}[/tex]This equation is exactly the same as the one given in the graph, so it will form a system with infinite solutions with it.
4.
[tex]\begin{gathered} y-3x=-3 \\ y-3x+3x=3x-3 \\ y=3x-3 \end{gathered}[/tex]This equation has the same slope but a different y-intercept than the given equation, which means that they are parallel. A system formed between this option and the given line would have no solutions since both lines are parallel.
The only equation which will form a system with infinite equations with the one shown in the graph is number 3. y-3x+1=0