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)
$$
Remaining Attempts : 3
Skip to navigation

Answer 1

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 \( \boxed{7} \).