Express the equation `4x-5y+20=0` in the form so that:
(i) x is dependent variable and y is the independent variable.
(ii) y is dependent variable and x is independent variable.

Answer

To solve the equation \(4x - 5y + 20 = 0\) in the required forms, we will follow these steps:

### Step 1: Expressing x as a dependent variable and y as an independent variable

1. Start with the original equation:
\[ 4x - 5y + 20 = 0 \]

2. Rearrange the equation to isolate \(x\):
\[ 4x = 5y - 20 \]

3. Divide by 4 to solve for \(x\):
\[ x = \frac{5y - 20}{4} \]

4. Simplify the equation:
\[ x = \frac{5}{4}y - 5 \]

Now, we have expressed \(x\) as a dependent variable in terms of \(y\):
\[ x = \frac{5}{4}y - 5 \]

### Step 2: Expressing y as a dependent variable and x as an independent variable

1. Start again with the original equation:
\[ 4x - 5y + 20 = 0 \]

2. Rearrange the equation to isolate \(y\):
\[ -5y = -4x - 20 \]

3. Multiply through by -1:
\[ 5y = 4x + 20 \]

4. Divide by 5 to solve for \(y\):
\[ y = \frac{4x + 20}{5} \]

5. Simplify the equation:
\[ y = \frac{4}{5}x + 4 \]

Now, we have expressed \(y\) as a dependent variable in terms of \(x\):
\[ y = \frac{4}{5}x + 4 \]

### Final Results:
- For \(x\) as a dependent variable and \(y\) as an independent variable:
\[ x = \frac{5}{4}y - 5 \]

- For \(y\) as a dependent variable and \(x\) as an independent variable:
\[ y = \frac{4}{5}x + 4 \]