Write down the equation of the straight line cuttting off intercepts a and b from the axes where
a = 5, b = -6

Answer

To find the equation of the straight line that cuts off intercepts \( a \) and \( b \) from the axes, where \( a = 5 \) and \( b = -6 \), we can follow these steps:

### Step 1: Identify the intercepts
We are given:
- \( a = 5 \) (x-intercept)
- \( b = -6 \) (y-intercept)

### 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 \( b \):
\[ \frac{x}{5} + \frac{y}{-6} = 1 \]

### Step 3: Simplify the equation
We can rewrite the equation as:
\[ \frac{x}{5} - \frac{y}{6} = 1 \]

### Step 4: Clear the denominators
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 30:
\[ 30 \left(\frac{x}{5}\right) - 30 \left(\frac{y}{6}\right) = 30 \cdot 1 \]
This simplifies to:
\[ 6x - 5y = 30 \]

### Step 5: Rearranging the equation
We can rearrange this equation to the standard form:
\[ 6x - 5y - 30 = 0 \]

### Final Equation
Thus, the equation of the straight line that cuts off intercepts \( a = 5 \) and \( b = -6 \) from the axes is:
\[ 6x - 5y - 30 = 0 \]

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