The problem states that the equation of the line on the graph represents a direct variation equation, and it asks for the constant of variation.

Step 1: Understanding Direct Variation

A direct variation equation has the form: $y = kx$ where $k$ is the constant of variation (also known as the constant of proportionality).

Step 2: Extracting the Equation

From the image, the equation given appears to be: $y = \frac{3}{2} x$ which is already in the form $y = kx$.

Step 3: Identifying the Constant of Variation

Comparing with $y = kx$, we see that: $k = \frac{3}{2}$

Final Answer:

The constant of variation is $\frac{3}{2}$.

Would you like further explanation?

Related Questions:

1. What does the constant of variation represent in a real-world scenario?
2. How do you determine if an equation represents direct variation?
3. What happens to the graph if the constant of variation is negative?
4. Can a direct variation equation pass through the y-axis at a nonzero point?
5. How does the value of $k$ affect the steepness of the graph?

Tip:

In a direct variation, the graph always passes through the origin $(0,0)$. If a line does not pass through the origin, it is not a direct variation equation.