Identify the constant of proportionality from the graph.
In order to identify the constant of proportionality from a graph, we need a graph that represents a direct proportionality relationship. A direct proportionality means that as one variable increases, the other variable also increases at a constant rate.
If the graph is a straight line passing through the origin (0,0), then the slope of the line represents the constant of proportionality. The slope is the ratio of the vertical change (y-axis) to the horizontal change (x-axis) between any two points on the line.
Therefore, the constant of proportionality can be found by determining the slope of the line on the graph.
Graphs of Proportional Relationships Quick Check 1 of 51 of 5 Items Question Use the image to answer the question Identify the constant of proportionality from the graph. (1 point)
To identify the constant of proportionality from a graph, you will need to examine the relationship between the variables plotted. The constant of proportionality is represented by the slope of the graph.
If the graph shows a direct proportionality, meaning that the variables increase or decrease together at a constant rate, the constant of proportionality is equal to the slope of the line. This can be calculated by determining the change in the y-values divided by the change in the x-values (rise over run).
For example, if the graph shows a linear relationship and the slope of the line is 3, then the constant of proportionality is 3.
However, if the graph shows an inverse proportionality, meaning that one variable increases while the other decreases at a constant rate, the constant of proportionality is equal to the negative value of the slope.
Therefore, to identify the constant of proportionality, you need to determine the slope of the graph.
To identify the constant of proportionality from a graph, you need to determine the slope of the line. The constant of proportionality represents the ratio between the dependent variable and the independent variable in a proportional relationship.
Here are the steps to find the constant of proportionality from a graph:
1. Look for a linear relationship: Ensure that the graph represents a linear relationship, where the dependent and independent variables are in direct proportion.
2. Identify two points: Select any two points on the line. It can be any two points as long as they lie on the line.
3. Calculate the slope: Use the formula for calculating the slope of a line, which is given by the change in the y-coordinates divided by the change in the x-coordinates (rise over run). The formula is as follows:
slope = (y₂ - y₁) / (x₂ - x₁)
Here, (x₁, y₁) and (x₂, y₂) represent the coordinates of the two points you identified.
4. Interpret the slope: The value of the slope represents the constant of proportionality. It indicates how much the dependent variable changes for each unit change in the independent variable. Therefore, the slope is the constant of proportionality.
By following these steps and calculating the slope, you can identify the constant of proportionality from a graph.