To determine which graph shows that the linear system \(3x + 2y = 12\) and \(6x + 4y = 24\) has an infinite number of solutions, we need to note that the two equations represent the same line. This means that their graphs will overlap completely, showing that every point on the line is a solution to both equations.
After analyzing the graph descriptions:
- The first graph shows only one line.
- The second graph shows two intersecting lines, indicating a unique solution.
- The third graph shows two parallel lines, indicating no solutions.
- The fourth graph shows only one line.
Out of these options, none actually indicate two overlapping lines because each graph describes either a single line or two separate lines.
However, since the equations \(3x + 2y = 12\) and \(6x + 4y = 24\) are multiples of each other (the second equation can be derived from the first by multiplying it by 2), they represent the same line. Therefore, if there were a graph depicting this, it would simply show one line or two overlapping lines.
Given the descriptions provided, it seems that:
- The response indicating two lines that are parallel would not suffice for infinite solutions,
- A graph showing two intersecting lines would not suffice,
- The best fit could possibly be described by the first or fourth graphs (though they show a single line).
Thus, based on reading the options, it seems none indicate the correct scenario of infinite solutions expressed as overlapping lines, but you would typically look for a graph that shows one line only, indicating \(3x + 2y = 12\) is the same as \(6x + 4y = 24\).
Answer: Choose the graph that shows a single line, either the first or the fourth (both indicate only one line).