Find the equation of the line whose x-intercept is 8 and y-intercept is -12.

Answer

To find the equation of the line whose x-intercept is 8 and y-intercept is -12, we can follow these steps:

### Step 1: Identify the intercepts
The x-intercept is the point where the line crosses the x-axis, which is given as (8, 0). The y-intercept is the point where the line crosses the y-axis, which is given as (0, -12).

### Step 2: Use the two-point form of the equation of a line
The two points we have are:
- Point A (8, 0) - x-intercept
- Point B (0, -12) - y-intercept

The formula for the equation of a line passing through two points (x1, y1) and (x2, y2) is:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1) \]

### Step 3: Substitute the points into the formula
Here, we can let:
- \( (x_1, y_1) = (8, 0) \)
- \( (x_2, y_2) = (0, -12) \)

Substituting these values into the formula gives:
\[ y - 0 = \frac{-12 - 0}{0 - 8} (x - 8) \]

### Step 4: Simplify the equation
This simplifies to:
\[ y = \frac{-12}{-8} (x - 8) \]
\[ y = \frac{12}{8} (x - 8) \]
\[ y = \frac{3}{2} (x - 8) \]

### Step 5: Distribute and rearrange
Distributing the right side:
\[ y = \frac{3}{2}x - \frac{3}{2} \times 8 \]
\[ y = \frac{3}{2}x - 12 \]

### Step 6: Rearranging to standard form
To convert this to standard form \( Ax + By + C = 0 \):
\[ \frac{3}{2}x - y - 12 = 0 \]
Multiplying through by 2 to eliminate the fraction:
\[ 3x - 2y - 24 = 0 \]
Rearranging gives:
\[ 3x - 2y = 24 \]

### Final Equation
Thus, the equation of the line is:
\[ 3x - 2y = 24 \]

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