Final answer:
A proportional relationship is graphed as a straight line passing through the origin, and Option 2 is correct. However, not all points may represent reasonable solutions due to practical limits in real-world scenarios.
Step-by-step explanation:
Understanding Proportional Relationships and Their Graphs
In a proportional relationship, two variables are directly proportional to each other, meaning that as one variable changes, the other changes at a constant rate. When graphed, a proportional relationship is represented by a straight line that passes through the origin (0,0). This line is also known as the line of proportionality. The fact that the line passes through the origin reflects the idea that if one variable is zero, so is the other. Option 2 is correct: The graph will be a straight line going through the origin, and each point may not be a reasonable solution. While the mathematical relationship itself includes all points on the line, in real-world situations, not all of these points may represent practical or realistic values.
For example, a graph showing the relationship between time spent studying and the amount of information learned would go through the origin because if no time is spent studying, presumably no information is learned. However, not every point on this line would necessarily represent a reasonable solution because, after a certain number of hours, additional studying might not lead to more learning due to fatigue, indicating practical limits to the relationship.
Graphs provide a visual illustration of data, showing patterns, trends, and comparisons. A line graph is often used to depict such relationships between variables. It's important, however, to interpret these graphs within the context of real-world constraints, recognizing that while a mathematical model may suggest an infinite set of possibilities, practical scenarios dictate a more limited range of plausible solutions.