Use the image to answer the question.

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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1 answer

To find the constant of proportionality in the given plotted points, we can use the formula for direct variation, which is typically represented as \( y = kx \), where \( k \) is the constant of proportionality.

From the points provided:

  • (0, 0)
  • (2, 14)
  • (4, 28)
  • (6, 42)
  • (8, 56)
  • (10, 70)
  • (12, 84)

We can calculate \( k \) by choosing one of the non-zero points, for example, (2, 14).

Using the point (2, 14): \[ y = kx \implies 14 = k(2) \] Solving for \( k \): \[ k = \frac{14}{2} = 7 \]

To ensure consistency, let's verify the value of \( k \) with a couple more points.

For the point (4, 28): \[ y = kx \implies 28 = k(4) \] \[ k = \frac{28}{4} = 7 \]

For the point (6, 42): \[ y = kx \implies 42 = k(6) \] \[ k = \frac{42}{6} = 7 \]

These checks confirm that the constant of proportionality \( k \) remains consistent across these points.

Thus, the constant of proportionality for this graph is: \[ \boxed{7} \]