Graphs of Proportional Relationships Practice

Question

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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.
K=
(1 point)
$$

Answer 1

To find the constant of proportionality (K) from the given points, we can use the formula for the constant of proportionality in a linear relationship which is defined as:

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

We can take any of the provided points to calculate K. The points provided include:

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

Let's use the point (2, 14) as an example:

\[ K = \frac{y}{x} = \frac{14}{2} = 7 \]

To confirm that this constant applies for all points, we can check a few more points:

For the point (4, 28):

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

For the point (6, 42):

\[ K = \frac{42}{6} = 7 \]

For the point (8, 56):

\[ K = \frac{56}{8} = 7 \]

For the point (10, 70):

\[ K = \frac{70}{10} = 7 \]

For the point (12, 84):

\[ K = \frac{84}{12} = 7 \]

Since all points yield a constant of proportionality (K) of 7, we can conclude that:

K = 7.