To find the constant of proportionality in a graph, you first need to identify whether the graph represents a proportional relationship. A proportional relationship will have a straight line passing through the origin (0,0). If this is the case, the constant of proportionality can be found by determining the ratio of the corresponding values on the axes.
Here are the steps to follow:
- Identify the axes: Look at the x-axis and y-axis to see what quantities are being represented. For example, the x-axis could represent distance, while the y-axis represents time.
- Choose two points on the line: Select two points on the line that are easy to read. For example, you may choose (2, 4) and (4, 8).
- Calculate the ratio: Use the coordinates of the two points to calculate the constant of proportionality, which is the slope of the line. The formula is:
k = y / x
Continuing with our example, if we take the point (2, 4):
k = 4 / 2 = 2
Hence, the constant of proportionality is 2. You can verify this with the second point (4, 8):
k = 8 / 4 = 2
Both points yield the same constant.
In summary, the constant of proportionality is simply the ratio of the dependent variable to the independent variable at any point along the line on the graph, provided the relationship is proportional. This value helps to describe the relationship between the two quantities represented in the graph.