The line, represented by the equation `3x - 8y = 2`, passes through the point (k, 2). Find the value of k.

Answer

To find the value of \( k \) such that the line represented by the equation \( 3x - 8y = 2 \) passes through the point \( (k, 2) \), we can follow these steps:

### Step 1: Substitute the point into the line equation
We know that if the point \( (k, 2) \) lies on the line, then substituting \( x = k \) and \( y = 2 \) into the line equation should satisfy it. The line equation is:
\[ 3x - 8y = 2 \]
Substituting \( x = k \) and \( y = 2 \):
\[ 3(k) - 8(2) = 2 \]

### Step 2: Simplify the equation
Now, simplify the left-hand side:
\[ 3k - 16 = 2 \]

### Step 3: Solve for \( k \)
Next, we need to isolate \( k \). We can do this by adding 16 to both sides of the equation:
\[ 3k = 2 + 16 \]
\[ 3k = 18 \]

Now, divide both sides by 3:
\[ k = \frac{18}{3} \]
\[ k = 6 \]

### Conclusion
Thus, the value of \( k \) is \( 6 \).

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