Answer:
The graph of a proportional relationship can be described by the following statements:
1. The graph passes through the origin (0, 0). This means that when the input (x-value) is zero, the output (y-value) is also zero.
2. The graph is a straight line. This indicates that the relationship between the input and output variables is constant.
3. The slope of the line is constant. The slope represents the rate of change between the input and output variables. In a proportional relationship, the rate of change is always the same. For example, if the slope is 2, it means that for every unit increase in the input, the output also increases by 2 units.
4. The line extends infinitely in both directions. This implies that the relationship between the input and output variables continues indefinitely without any restrictions or limitations.
Here's an example to help illustrate these statements:
Let's say you're measuring the time it takes to run a certain distance. If the relationship between the time (in minutes) and the distance (in miles) is proportional, the graph would satisfy the statements mentioned above. For instance, if it takes 10 minutes to run 1 mile, then it would take 20 minutes to run 2 miles, 30 minutes to run 3 miles, and so on. The graph would show a straight line passing through the origin with a constant slope of 10 (since each additional mile adds 10 minutes to the time).
Remember that a proportional relationship implies that the ratio between the input and output variables remains constant.
Explanation: