Suppose that y is inversely proportional to x.

Find the constant of proportionality  
k
  if  
y
=
4
  when  
x
=
9
 .
k
=
  

Using the  
k
  from above write the variation equation in terms of  
x
 .
y
=
  

Using the  
k
  from above find  
y
  given that  
x
  = 17.
y
=

If \( y \) is inversely proportional to \( x \), this means that:

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

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

### Step 1: Find \( k \) given \( y = 4 \) when \( x = 9 \)

Using the given values:
\[
4 = \frac{k}{9}
\]

Solving for \( k \):
\[
k = 4 \times 9 = 36
\]

So, the constant of proportionality \( k = 36 \).

### Step 2: Write the variation equation in terms of \( x \)

Using \( k = 36 \), the equation becomes:
\[
y = \frac{36}{x}
\]

### Step 3: Find \( y \) when \( x = 17 \)

Substitute \( x = 17 \) into the equation:
\[
y = \frac{36}{17}
\]

So,
\[
y \approx 2.12
\]

### Summary:
- **Constant of proportionality** \( k = 36 \)
- **Variation equation**: \( y = \frac{36}{x} \)
- **\( y \) when \( x = 17 \)**: \( y \approx 2.12 \)

Would you like further explanation or details?

#### Related Questions:
1. What happens to \( y \) as \( x \) approaches infinity in an inverse variation?
2. How does the graph of \( y = \frac{36}{x} \) look compared to a linear function?
3. Can \( y \) ever be zero in an inverse variation?
4. If \( y \) is inversely proportional to \( x^2 \), how would the equation change?
5. How would the constant \( k \) change if \( y = 5 \) when \( x = 7 \)?

#### Tip:
In inverse variation, as one variable increases, the other decreases at a rate determined by \( k \), showing the concept of proportional balancing.

Suppose that y is inversely proportional to x. Find the constant of proportionality k if y = 4 when x = 9. k = ? Using the k from above, write the variation equation in terms of x. y = ? Using the k from above, find y given that x = 17. y = ?

Solve an inverse proportion problem by finding the constant of proportionality k when y = 4 and x = 9. Write the variation equation and calculate y when x = 17. This problem involves core algebra concepts, including inverse proportion relationships and variation equations. Suitable for students in Grades 8-10.

Math Problem Statement

Find the constant of proportionality
k if
y

4 when
x

9 . k

Using the
k from above write the variation equation in terms of
x . y

Using the
k from above find
y given that
x = 17. y

Solution

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