If the equation 3y=7 is expressed as ax+by+c=0 then which of the following is correct

Options

A. a=0,b=7,c=3
B. a=3,b=0,c=-7
C. a=0,b=3,c=-7
D. a=3,b=-7,c=0

Answer

To express the equation \(3y = 7\) in the form \(ax + by + c = 0\), we can follow these steps:

### Step 1: Start with the given equation
We have the equation:
\[ 3y = 7 \]

### Step 2: Rearrange the equation
To express this in the standard form \(ax + by + c = 0\), we need to move all terms to one side of the equation. We can do this by subtracting \(7\) from both sides:
\[ 3y - 7 = 0 \]

### Step 3: Introduce the \(x\) term
Since there is no \(x\) term in the original equation, we can add \(0x\) to the left side:
\[ 0x + 3y - 7 = 0 \]

### Step 4: Identify coefficients
Now, we can identify the coefficients \(a\), \(b\), and \(c\):
- \(a = 0\) (coefficient of \(x\))
- \(b = 3\) (coefficient of \(y\))
- \(c = -7\) (constant term)

### Step 5: Write the final equation
Thus, the equation in the form \(ax + by + c = 0\) is:
\[ 0x + 3y - 7 = 0 \]

### Conclusion
From the above steps, we find:
- \(a = 0\)
- \(b = 3\)
- \(c = -7\)