To determine the constant of proportionality from a graph, you will need to analyze the relationship between the two variables depicted in the graph. The constant of proportionality (k) can typically be found using the formula:
\[ y = kx \]
Where \( y \) is the dependent variable and \( x \) is the independent variable. The constant of proportionality \( k \) is the ratio of \( y \) to \( x \) for any point on the graph:
\[ k = \frac{y}{x} \]
Here’s how to find it:
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Choose any point on the graph, ideally one with integer coordinates for simplicity. Let's say the point you choose has coordinates \( (x_1, y_1) \).
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Calculate the value of the constant of proportionality by dividing:
\[ k = \frac{y_1}{x_1} \]
- If the graph is indeed a proportional relationship, this ratio should be constant for all points. You can verify this by choosing another point \( (x_2, y_2) \) and checking if:
\[ k = \frac{y_2}{x_2} \]
If both equations yield the same \( k \), then that is your constant of proportionality.
Please refer to the specific points shown on the graph in your case to perform the calculations as needed. If you share the coordinates of the points, I can assist you further in calculating the constant.
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