The equation of a line which passes through points P(4,0) and Q(0,-3) will be

Options

A. `x/4 +xy/3 =1`
B. `x/3-y/4=7`
C. `x/4 - y/3 =1`
D. `x/3 + y/4 =7`

Answer

To find the equation of the line passing through the points P(4, 0) and Q(0, -3), we can use the point-slope form of the equation of a line. Here’s a step-by-step solution:

### Step 1: Identify the coordinates of the points
Let the coordinates of point P be \( (x_1, y_1) = (4, 0) \) and the coordinates of point Q be \( (x_2, y_2) = (0, -3) \).

### Step 2: Calculate the slope (m) of the line
The slope \( m \) of the line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values:
\[ m = \frac{-3 - 0}{0 - 4} = \frac{-3}{-4} = \frac{3}{4} \]

### Step 3: Use the point-slope form of the equation
The point-slope form of the equation of a line is:
\[ y - y_1 = m(x - x_1) \]
Using point P(4, 0) and the slope \( m = \frac{3}{4} \):
\[ y - 0 = \frac{3}{4}(x - 4) \]

### Step 4: Simplify the equation
Distributing the slope on the right side:
\[ y = \frac{3}{4}x - \frac{3}{4} \times 4 \]
\[ y = \frac{3}{4}x - 3 \]

### Step 5: Rearranging to standard form
To rearrange this into standard form \( Ax + By + C = 0 \):
\[ \frac{3}{4}x - y - 3 = 0 \]
Multiplying through by 4 to eliminate the fraction:
\[ 3x - 4y - 12 = 0 \]
Rearranging gives:
\[ 3x - 4y = 12 \]

### Final Answer
The equation of the line is:
\[ 3x - 4y = 12 \]

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