Using the points shown in the graph, identify the constant of proportionality for this graph.
To find the constant of proportionality for a graph, we need to determine the ratio between the change in the dependent variable (y) and the change in the independent variable (x). Let's identify two points from the graph and calculate the ratio.
From the graph, let's choose two points, such as (1,7) and (3,21).
The change in y can be calculated as follows:
Δy = y2 - y1 = 21 - 7 = 14
The change in x can be calculated as follows:
Δx = x2 - x1 = 3 - 1 = 2
Now, let's calculate the ratio:
Δy / Δx = 14 / 2 = 7
Therefore, the constant of proportionality for this graph is 7.
To identify the constant of proportionality for a graph, we need to determine the ratio of the vertical change (y-values) to the corresponding horizontal change (x-values) between any two points on the graph.
Let's say we have two points on the graph:
Point A: (x1, y1)
Point B: (x2, y2)
The constant of proportionality, denoted as k, can be found by calculating the ratio of the vertical change (y2 - y1) to the corresponding horizontal change (x2 - x1):
k = (y2 - y1) / (x2 - x1)
Once we calculate this ratio for any two points on the graph, it will give us the constant of proportionality.
To determine the constant of proportionality for this graph, we need to look at the relationship between the x-values and the corresponding y-values.
In a proportional relationship, the ratio of the y-values to the x-values should be a constant value. Let's calculate the ratio for each point:
Point A: (1, 2) --> ratio = 2/1 = 2
Point B: (2, 4) --> ratio = 4/2 = 2
Point C: (3, 6) --> ratio = 6/3 = 2
As we can see, the ratio of the y-values to the x-values is consistently equal to 2 for all the points. Therefore, the constant of proportionality for this graph is 2.