Express the linear equation `sqrt(2x) -4=5y` in the form of ax+by +c=0 and thus indicate the values of a,b and c

Answer

To express the linear equation \( \sqrt{2x} - 4 = 5y \) in the form \( ax + by + c = 0 \), we will follow these steps:

### Step 1: Start with the given equation
The given equation is:
\[ \sqrt{2x} - 4 = 5y \]

### Step 2: Rearrange the equation
We want to move all terms to one side of the equation. We can do this by subtracting \( 5y \) from both sides:
\[ \sqrt{2x} - 4 - 5y = 0 \]

### Step 3: Rewrite the equation
Now, we can rewrite the equation in the form \( ax + by + c = 0 \):
\[ \sqrt{2} \cdot x - 5y - 4 = 0 \]

### Step 4: Identify coefficients
From the equation \( \sqrt{2} \cdot x - 5y - 4 = 0 \), we can identify the coefficients:
- \( a = \sqrt{2} \)
- \( b = -5 \)
- \( c = -4 \)

### Final Result
Thus, the equation in the form \( ax + by + c = 0 \) is:
\[ \sqrt{2} \cdot x - 5y - 4 = 0 \]
And the values are:
- \( a = \sqrt{2} \)
- \( b = -5 \)
- \( c = -4 \)

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