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)
$$

Answer 1

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:
\[
\boxed{7}
\]