Write down the equation of the straight line cuttting off intercepts a and b from the axes where
a = -2, b = 3

Answer

To find the equation of the straight line that cuts off intercepts \( a \) and \( b \) from the axes, where \( a = -2 \) and \( b = 3 \), we can follow these steps:

### Step 1: Understand the intercepts
The x-intercept \( a \) is given as -2, which means the line crosses the x-axis at the point (-2, 0). The y-intercept \( b \) is given as 3, meaning the line crosses the y-axis at the point (0, 3).

### Step 2: Use the intercept form of the equation of a line
The equation of a line in intercept form is given by:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]
Substituting the values of \( a \) and \( b \):
\[ \frac{x}{-2} + \frac{y}{3} = 1 \]

### Step 3: Clear the fractions
To eliminate the fractions, we can multiply through by the least common multiple (LCM) of the denominators, which is 6:
\[ 6 \left( \frac{x}{-2} \right) + 6 \left( \frac{y}{3} \right) = 6 \]
This simplifies to:
\[ -3x + 2y = 6 \]

### Step 4: Rearrange the equation
To express the equation in a more standard form, we can rearrange it:
\[ 2y - 3x = 6 \]
or
\[ 3x - 2y = -6 \]

### Step 5: Final equation
Thus, the equation of the straight line is:
\[ 3x - 2y - 6 = 0 \]

### Summary of the steps:
1. Identify the intercepts from the problem statement.
2. Substitute the intercepts into the intercept form of the line equation.
3. Multiply through by the LCM to eliminate fractions.
4. Rearrange the equation to standard form.