Equation of straight line passing through the points `(2,0) and (0, -3)` is

Options

A. `(x)/(2) - (y)/(3) =1`
B. `(y)/(3) - (x)/(2) =1`
C. `(x)/(3) - (y)/(2) = 1`
D. `(y)/(2) - (x)/(3) =1 `

Answer

To find the equation of the straight line passing through the points (2, 0) and (0, -3), we can follow these steps:

### Step 1: Identify the coordinates of the points
Let the points be:
- Point A (x1, y1) = (2, 0)
- Point B (x2, y2) = (0, -3)

### Step 2: Use the formula for the equation of a line
The equation of a line passing through two points (x1, y1) and (x2, y2) can be given by the formula:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1) \]

### Step 3: Substitute the coordinates into the formula
Substituting the coordinates of points A and B into the formula:
- \(y_1 = 0\)
- \(y_2 = -3\)
- \(x_1 = 2\)
- \(x_2 = 0\)

We get:
\[ y - 0 = \frac{-3 - 0}{0 - 2} (x - 2) \]
This simplifies to:
\[ y = \frac{-3}{-2} (x - 2) \]

### Step 4: Simplify the equation
Calculating the fraction:
\[ y = \frac{3}{2} (x - 2) \]
Distributing the \(\frac{3}{2}\):
\[ y = \frac{3}{2}x - 3 \]

### Step 5: Rearranging to standard form
To convert this to standard form, we can multiply through by 2 to eliminate the fraction:
\[ 2y = 3x - 6 \]
Rearranging gives:
\[ 3x - 2y - 6 = 0 \]
Or, in the form \(Ax + By + C = 0\):
\[ 3x - 2y = 6 \]

### Step 6: Convert to the required form
We can rearrange this to:
\[ \frac{x}{2} - \frac{y}{3} = 1 \]

### Final Answer
Thus, the equation of the straight line passing through the points (2, 0) and (0, -3) is:
\[ \frac{x}{2} - \frac{y}{3} = 1 \]