To identify the constant of proportionality from a graph, you need to first understand what a constant of proportionality represents. In a proportional relationship between two variables, the ratio of their corresponding values remains constant. This constant ratio is called the constant of proportionality.
To find the constant of proportionality from the graph, follow these steps:
1. Determine the two variables involved in the proportional relationship. Typically, these are represented on the x-axis and y-axis of the graph.
2. Identify any data points on the graph that lie on a straight line. A proportional relationship is graphically represented by a straight line passing through the origin (0,0).
3. Select two points on the line and determine their coordinates. Take note of the x and y values for each point.
4. Calculate the ratio of the y-coordinate to the x-coordinate for both points. This will give you the corresponding values of the constant of proportionality between the variables.
5. Compare the ratios calculated for the different points. If there is a proportional relationship, the ratios should be equal or very close to each other.
6. Once you have obtained the ratios, take the average of the values to find a more accurate estimation of the constant of proportionality.
Remember that some graphs may not show a proportional relationship between the variables, so it's crucial to analyze the linearity of the graph before attempting to find the constant of proportionality.