Check, whether point (4, -2) lies on the line represented by equation `3x + 5y = 2` or not? 

Answer

To determine whether the point \( (4, -2) \) lies on the line represented by the equation \( 3x + 5y = 2 \), we will substitute the coordinates of the point into the equation and check if both sides are equal.

### Step-by-Step Solution:

1. **Identify the point and the equation of the line:**
- The point is \( P(4, -2) \).
- The equation of the line is \( 3x + 5y = 2 \).

2. **Substitute the coordinates of the point into the equation:**
- Here, \( x = 4 \) and \( y = -2 \).
- Substitute these values into the left-hand side (LHS) of the equation:
\[ LHS = 3(4) + 5(-2) \]

3. **Calculate the LHS:**
- First, calculate \( 3(4) \):
\[ 3(4) = 12 \]
- Next, calculate \( 5(-2) \):
\[ 5(-2) = -10 \]
- Now, combine these results:
\[ LHS = 12 - 10 = 2 \]

4. **Compare LHS with the right-hand side (RHS):**
- The RHS of the equation is \( 2 \).
- We found that \( LHS = 2 \).

5. **Conclusion:**
- Since \( LHS = RHS \) (both equal to 2), we conclude that the point \( (4, -2) \) lies on the line represented by the equation \( 3x + 5y = 2 \).

### Final Answer:
Yes, the point \( (4, -2) \) lies on the line.