Use the image to answer the question.

Question

A graph shows an x-axis ranging from 0 to 12 in increments of 2 and a y-axis ranging from 0 to 84 in increments of 14.

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 \( k \) from the graph, you need to identify a point on the graph that represents a proportional relationship. Proportional relationships can be expressed as \( y = kx \), where \( k \) is the constant of proportionality.

1. Find a point (x, y) on the graph. (For example, if you have the point (2, 28)):

   • Here \( x = 2 \) and \( y = 28 \).

2. Use the formula \( k = \frac{y}{x} \): \[ k = \frac{28}{2} = 14 \]

3. Repeat this process for additional points to confirm consistency. For example:

   • If you have another point like (4, 56): \[ k = \frac{56}{4} = 14 \]

If all points yield the same \( k \), then that is the constant of proportionality.

Based on this, the constant of proportionality \( k \) is: \[ k = 14 \]

You should adjust the numbers based on the specific points shown in the graph if they differ from the examples given.