Find the value of k so that the point (2,5) lies on the line represented by `kx + 3y =1`.

Answer

To find the value of \( k \) so that the point \( (2, 5) \) lies on the line represented by the equation \( kx + 3y = 1 \), we can follow these steps:

### Step 1: Substitute the coordinates into the equation
Since the point \( (2, 5) \) lies on the line, we can substitute \( x = 2 \) and \( y = 5 \) into the equation \( kx + 3y = 1 \).

\[ k(2) + 3(5) = 1 \]

### Step 2: Simplify the equation
Now, we simplify the left side of the equation:

\[ 2k + 15 = 1 \]

### Step 3: Isolate the term with \( k \)
Next, we need to isolate \( 2k \) by moving \( 15 \) to the right side of the equation:

\[ 2k = 1 - 15 \]

### Step 4: Calculate the right side
Now, we calculate the right side:

\[ 2k = -14 \]

### Step 5: Solve for \( k \)
Finally, we divide both sides by \( 2 \) to solve for \( k \):

\[ k = \frac{-14}{2} = -7 \]

### Conclusion
The value of \( k \) is \( -7 \).

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