Question

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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page 13 of 14

Answer 1

To identify the constant of proportionality from the given points, we can look for a consistent ratio of \( y \) to \( x \) for the points plotted.

The points given are:
- \( (0, 0) \)
- \( (2, 14) \)
- \( (4, 28) \)
- \( (6, 42) \)
- \( (8, 56) \)
- \( (10, 70) \)
- \( (12, 84) \)

We can calculate the ratio \( \frac{y}{x} \) for the non-zero points:

1. For \( (2, 14) \):
\[
\frac{14}{2} = 7
\]

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

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

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

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

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

All the ratios are consistent and equal to 7.

Therefore, the constant of proportionality for this graph is \( 7 \).