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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Remaining Attempts : 3
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1 answer

To identify the constant of proportionality from the given points, we first observe the coordinates of the plotted points. The format of the points is \( (x, y) \):

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

The constant of proportionality (k) is found by dividing \( y \) by \( x \) for any nonzero point:

For \( (2, 14) \): \[ k = \frac{y}{x} = \frac{14}{2} = 7 \]

For \( (4, 28) \): \[ k = \frac{28}{4} = 7 \]

For \( (6, 42) \): \[ k = \frac{42}{6} = 7 \]

For \( (8, 56) \): \[ k = \frac{56}{8} = 7 \]

For \( (10, 70) \): \[ k = \frac{70}{10} = 7 \]

For \( (12, 84) \): \[ k = \frac{84}{12} = 7 \]

In all cases, the constant of proportionality \( k \) is \( 7 \).

Therefore, the constant of proportionality for the graph is \( \boxed{7} \).