For what value of k will the point `(3,- k)` lie on the line `9x + 4y = 3` ?

Answer

To find the value of \( k \) for which the point \( (3, -k) \) lies on the line given by the equation \( 9x + 4y = 3 \), we can follow these steps:

### Step 1: Substitute the point into the line equation
We know that for the point \( (3, -k) \) to lie on the line, it must satisfy the equation of the line. We substitute \( x = 3 \) and \( y = -k \) into the equation \( 9x + 4y = 3 \).

\[ 9(3) + 4(-k) = 3 \]

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

\[ 27 - 4k = 3 \]

### Step 3: Solve for \( k \)
Next, we isolate \( k \) by moving the constant term to the right side:

\[ -4k = 3 - 27 \]

\[ -4k = -24 \]

Now, divide both sides by -4:

\[ k = \frac{-24}{-4} = 6 \]

### Conclusion
Thus, the value of \( k \) for which the point \( (3, -k) \) lies on the line \( 9x + 4y = 3 \) is:

\[ \boxed{6} \]