If x and y are directly proportional and when x = 13, y = 39, which of the following is not a possible pair of corresponding values of x and y ?

Options

A. 1 and 3
B. 17 and 51
C. 30 and 10
D. 6 and 18

Answer

To solve the problem step by step, we need to determine the relationship between x and y given that they are directly proportional.

### Step 1: Understand Direct Proportionality
When two variables x and y are directly proportional, it means that there exists a constant k such that:
\[ y = k \cdot x \]

### Step 2: Find the Constant of Proportionality
We are given that when \( x = 13 \), \( y = 39 \). We can use this information to find the constant k.
\[ y = k \cdot x \]
Substituting the known values:
\[ 39 = k \cdot 13 \]

### Step 3: Solve for k
To find k, we can rearrange the equation:
\[ k = \frac{39}{13} \]
Calculating this gives:
\[ k = 3 \]

### Step 4: Write the Relationship
Now that we have k, we can express the relationship between x and y:
\[ y = 3 \cdot x \]

### Step 5: Check Possible Pairs
Now we need to check which of the given pairs of (x, y) does not satisfy the equation \( y = 3 \cdot x \).

Let's evaluate the pairs:
1. If \( x = 1 \), then \( y = 3 \cdot 1 = 3 \) (This is a valid pair)
2. If \( x = 17 \), then \( y = 3 \cdot 17 = 51 \) (This is a valid pair)
3. If \( x = 10 \), then \( y = 3 \cdot 10 = 30 \) (This is a valid pair)
4. If \( x = 6 \), then \( y = 3 \cdot 6 = 18 \) (This is a valid pair)

### Step 6: Identify the Invalid Pair
Now, we will identify which pair does not satisfy the relationship:
- If \( x = 10 \), we calculated \( y \) to be 30, but if the given pair is (10, 10), then this does not satisfy \( y = 3 \cdot x \).

Thus, the pair that is not possible is (10, 10).

### Final Answer
The pair of corresponding values of x and y that cannot be is (10, 10).

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