The graph below shows a proportional relationship between 
\[x\] and 
\[y\].
What is the constant of proportionality, 
 
\[\dfrac{y}{x}\] ?
A graph on a Cartesian coordinate system with x and y-axes. The x-axis is marked with evenly spaced ticks in increments of 0.5, ranging from 0.5 to 4.5. The y-axis is marked with evenly spaced ticks in increments of 1, ranging from 1 to 9. The graph displays a single slant line starting from (0,0) with an arrowhead at its end. The line passes through a point marked with a filled dot at (1,3.5). The point (0,0) is marked with a filled dot as well.
\[\small{0.5}\]
\[\small{1}\]
\[\small{1.5}\]
\[\small{2}\]
\[\small{2.5}\]
\[\small{3}\]
\[\small{3.5}\]
\[\small{4}\]
\[\small{4.5}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{8}\]
\[\small{9}\]
\[y\]
\[x\]

To find the constant of proportionality, \(\dfrac{y}{x}\), we can use the coordinates of any point on the line, excluding \((0,0)\) since division by zero is undefined.

The graph passes through the point \((1, 3.5)\). Using this point, we can calculate the constant of proportionality as follows:

\[
\text{Constant of proportionality} = \dfrac{y}{x} = \dfrac{3.5}{1} = 3.5
\]

Thus, the constant of proportionality is \(3.5\).

Do you have any questions or would you like further clarification?

Here are 5 related questions you can explore:
1. How does the constant of proportionality affect the steepness of the line in a graph?
2. What would happen to the constant of proportionality if the line passed through a different point?
3. How do you calculate the slope of a line if the relationship is not proportional?
4. Can a proportional relationship have a negative constant of proportionality?
5. How would you graph a proportional relationship with a constant of proportionality equal to 2?

**Tip:** In a proportional relationship, the constant of proportionality is always the slope of the line passing through the origin!

The graph below shows a proportional relationship between x and y. What is the constant of proportionality, y/x? A graph on a Cartesian coordinate system with x and y-axes. The x-axis is marked with evenly spaced ticks in increments of 0.5, ranging from 0.5 to 4.5. The y-axis is marked with evenly spaced ticks in increments of 1, ranging from 1 to 9. The graph displays a single slant line starting from (0,0) with an arrowhead at its end. The line passes through a point marked with a filled dot at (1,3.5). The point (0,0) is marked with a filled dot as well.

Learn how to determine the constant of proportionality y/x using a graph that shows a proportional relationship between x and y. This example features a graph passing through the origin (0,0) and the point (1,3.5), making it easy to understand the concept of proportional relationships and slopes. Perfect for students in Grades 6-8.

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