Use the image to answer the question.
A graph shows an x-axis ranging from 0 to 12 in increments of 2 and a y-axis ranging from 0 to 84 in increments of 14. A line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 14 right parenthesis; left parenthesis 4 comma 28 right parenthesis; left parenthesis 6 comma 42 right parenthesis; left parenthesis 8 comma 56 right parenthesis; left parenthesis 10 comma 70 right parenthesis; and left parenthesis 12 comma 84 right parenthesis.
Using the points shown in the graph, identify the constant of proportionality for this graph.
(1 point)
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To find the constant of proportionality for a line, we need to determine the relationship between the x-values and the y-values.
Looking at the given points, we can observe that the y-values increase by 14 each time the x-value increases by 2.
Therefore, the constant of proportionality for this graph is:
$$
\text{Constant of Proportionality} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{14}{2} = 7
$$
So, the constant of proportionality for this graph is 7.
The constant of proportionality for this graph can be found by calculating the ratio of the y-values to the x-values. We can choose any two points on the line to do this.
Let's choose the points (0, 0) and (2, 14). The ratio of the y-values (14) to the x-values (2) is 14/2 = 7.
Therefore, the constant of proportionality for this graph is 7.
To find the constant of proportionality for this graph, we need to examine the relationship between the x-values and the corresponding y-values. The constant of proportionality is the ratio of the y-values to the x-values.
Let's take two points on the line, (2, 14) and (4, 28). The change in y-values is 28 - 14 = 14, and the change in x-values is 4 - 2 = 2.
So, the ratio of the change in y to the change in x is 14/2 = 7.
We can do the same calculation for the other pairs of points and we will find that the ratio is always 7.
Therefore, the constant of proportionality for this graph is 7.