The straight line represented by equation `x - 3y + 8 = 0 ` passes through (2, 4). Is this true ? 

Answer

To determine whether the straight line represented by the equation \( x - 3y + 8 = 0 \) passes through the point \( (2, 4) \), we will substitute the coordinates of the point into the equation of the line and check if the equation holds true.

### Step-by-Step Solution:

1. **Write down the equation of the line:**
\[ x - 3y + 8 = 0 \]

2. **Identify the coordinates of the point:**
The point given is \( (2, 4) \), where \( x = 2 \) and \( y = 4 \).

3. **Substitute the coordinates into the equation:**
Replace \( x \) with \( 2 \) and \( y \) with \( 4 \) in the equation:
\[ 2 - 3(4) + 8 = 0 \]

4. **Calculate the left-hand side (LHS):**
\[ 2 - 12 + 8 \]
Simplifying this:
\[ 2 - 12 = -10 \]
Then,
\[ -10 + 8 = -2 \]

5. **Compare LHS with the right-hand side (RHS):**
The RHS of the equation is \( 0 \). Now we have:
\[ \text{LHS} = -2 \quad \text{and} \quad \text{RHS} = 0 \]

6. **Conclusion:**
Since LHS \( (-2) \) is not equal to RHS \( (0) \), we conclude that the point \( (2, 4) \) does not lie on the line represented by the equation \( x - 3y + 8 = 0 \). Therefore, the statement is false.