Find the equation of the line which cuts off intercepts-3 and 5 on the x-axis and y-axis respectively.

Answer

To find the equation of the line that cuts off intercepts -3 and 5 on the x-axis and y-axis respectively, we can use the intercept form of the equation of a line. The intercept form is given by:

\[ \frac{x}{a} + \frac{y}{b} = 1 \]

where \(a\) is the x-intercept and \(b\) is the y-intercept.

### Step 1: Identify the intercepts
From the problem statement:
- The x-intercept \(a = -3\)
- The y-intercept \(b = 5\)

### Step 2: Substitute the intercepts into the intercept form
We substitute \(a\) and \(b\) into the intercept form equation:

\[ \frac{x}{-3} + \frac{y}{5} = 1 \]

### Step 3: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 15:

\[ 15 \left(\frac{x}{-3}\right) + 15 \left(\frac{y}{5}\right) = 15 \]

This simplifies to:

\[ -5x + 3y = 15 \]

### Step 4: Rearrange the equation
We can rearrange this equation to standard form. Adding \(5x\) to both sides gives:

\[ 3y = 5x + 15 \]

Now, we can write it in standard form:

\[ 5x - 3y + 15 = 0 \]

### Final Equation
Thus, the equation of the line is:

\[ 5x - 3y + 15 = 0 \]

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