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)
k = __

Answer 1

To find the constant of proportionality \( k \) for the points provided, we will use the coordinates of any of the points on the line. The points given are:

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

The constant of proportionality \( k \) can be determined by the formula:

\[
k = \frac{y}{x}
\]

We can calculate \( k \) using one of the points (except for the origin):

Using the point \( (2, 14) \):

\[
k = \frac{14}{2} = 7
\]

To ensure consistency, we can check another point, for example, \( (4, 28) \):

\[
k = \frac{28}{4} = 7
\]

This calculation holds for all points listed since the ratio of \( y \) to \( x \) will be constant.

Thus, the constant of proportionality is:

\[
k = 7
\]