The value of y is directly proportional to the value of x. When x=3/4, y=56 1/4. Write a direct variation equation for the data. What is the value of y when x=1/2

Since \( y \) is directly proportional to \( x \), we can express this relationship with the equation:

\[
y = kx
\]

where \( k \) is the constant of proportionality. 

### Step 1: Find \( k \)

Given \( x = \frac{3}{4} \) and \( y = 56 \frac{1}{4} = 56.25 \):

\[
56.25 = k \cdot \frac{3}{4}
\]

To solve for \( k \):

\[
k = \frac{56.25}{\frac{3}{4}} = 56.25 \cdot \frac{4}{3} = 75
\]

### Step 2: Write the direct variation equation

The equation becomes:

\[
y = 75x
\]

### Step 3: Find \( y \) when \( x = \frac{1}{2} \)

Now substituting \( x = \frac{1}{2} \):

\[
y = 75 \cdot \frac{1}{2} = 37.5
\]

### Summary

The direct variation equation is:

\[
y = 75x
\]

When \( x = \frac{1}{2} \), the value of \( y \) is:

\[
y = 37.5
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you determine if a relationship is a direct variation?
2. What happens to the value of \( y \) if \( x \) is doubled?
3. Can you provide examples of direct variation in real life?
4. How would the equation change if \( y \) was inversely proportional to \( x \)?
5. What is the graphical representation of this direct variation? 

**Tip:** Always convert mixed numbers to improper fractions for easier calculations.

The value of y is directly proportional to the value of x. When x=3/4, y=56 1/4. Write a direct variation equation for the data. What is the value of y when x=1/2?

Explore the direct variation relationship between x and y, where y is directly proportional to x. Learn how to derive the equation y = 75x, and find the value of y when x = 1/2, yielding y = 37.5. Suitable for students in Grades 6-8.

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