The relationship between x and y can be written as y = mx , where m is a constant. If y = 17 when x = a , what is the value of y when x = 2a ?

Explanation

To solve the problem step by step, we will follow the relationship given in the question and substitute the values accordingly.

### Step 1: Understand the relationship
The relationship between \( x \) and \( y \) is given by the equation:
\[ y = mx \]
where \( m \) is a constant.

### Step 2: Substitute the known values
We know that when \( x = a \), \( y = 17 \). We can substitute these values into the equation:
\[ 17 = ma \]

### Step 3: Solve for \( a \)
From the equation \( 17 = ma \), we can express \( a \) in terms of \( m \):
\[ a = \frac{17}{m} \]

### Step 4: Find \( y \) when \( x = 2a \)
Now, we need to find the value of \( y \) when \( x = 2a \). We substitute \( x = 2a \) into the original equation:
\[ y = m(2a) \]

### Step 5: Substitute the value of \( a \)
Now, substitute \( a = \frac{17}{m} \) into the equation:
\[ y = m(2 \cdot \frac{17}{m}) \]

### Step 6: Simplify the expression
Now simplify the equation:
\[ y = m \cdot \frac{34}{m} \]
The \( m \) cancels out:
\[ y = 34 \]

### Final Answer
Thus, the value of \( y \) when \( x = 2a \) is:
\[ \boxed{34} \]