Find the equation of the line, whose :
x-intercept = -4 and y-intercept = 6 

Answer

To find the equation of the line with the given x-intercept and y-intercept, we can use the intercept form of the equation of a line. Here’s a step-by-step solution:

### Step 1: Write the intercept form of the equation of a line.
The intercept form of the equation of a line is given by:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]
where \(a\) is the x-intercept and \(b\) is the y-intercept.

### Step 2: Substitute the given intercepts into the equation.
Given:
- x-intercept \(a = -4\)
- y-intercept \(b = 6\)

Substituting these values into the intercept form:
\[ \frac{x}{-4} + \frac{y}{6} = 1 \]

### Step 3: Simplify the equation.
We can rewrite the equation as:
\[ -\frac{x}{4} + \frac{y}{6} = 1 \]

### Step 4: Eliminate the fractions by finding a common denominator.
The least common multiple (LCM) of the denominators (4 and 6) is 12. Multiply the entire equation by 12 to eliminate the fractions:
\[ 12 \left(-\frac{x}{4}\right) + 12 \left(\frac{y}{6}\right) = 12 \cdot 1 \]
This simplifies to:
\[ -3x + 2y = 12 \]

### Step 5: Rearrange the equation to standard form.
We can rearrange the equation to standard form:
\[ 2y - 3x = 12 \]

### Final Equation:
Thus, the equation of the line is:
\[ 2y - 3x = 12 \]

---