The slope of the line `a^(2)X - a Y + 1 =0`, where a is constant, is

Options

A. `-a^(2)`
B. `-a`
C. a
D. None of these

Answer

To find the slope of the line given by the equation \( a^2X - aY + 1 = 0 \), we can follow these steps:

### Step 1: Rearrange the equation
We start with the equation:
\[ a^2X - aY + 1 = 0 \]
We want to rearrange this into the slope-intercept form \( Y = mX + c \).

### Step 2: Isolate the \( Y \) term
To isolate \( Y \), we can move the other terms to the right side of the equation:
\[ -aY = -a^2X - 1 \]

### Step 3: Divide by -a
Now, we divide the entire equation by \(-a\) to solve for \( Y \):
\[ Y = \frac{a^2}{a}X + \frac{1}{-a} \]
This simplifies to:
\[ Y = aX - \frac{1}{a} \]

### Step 4: Identify the slope
In the equation \( Y = aX - \frac{1}{a} \), the coefficient of \( X \) is the slope \( m \). Thus, we find:
\[ m = a \]

### Conclusion
The slope of the line \( a^2X - aY + 1 = 0 \) is \( a \).