Question

The equation of the straight line passing through the points \( (1, -5) \) and \( (-2, 4) \) is

• A. \( 3x - y + 2 = 0 \)
• B. \( 3x + y - 2 = 0 \)
• C. \( 3x - y - 2 = 0 \)
• D. \( 3x + y + 2 = 0 \)

Hint:

To find the equation of a line passing through two points, use the point-slope form and simplify.

Answer 1

The Correct Option is D

The equation of the line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ y - y_1 = m(x - x_1), \] where \( m \) is the slope, calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1}. \] For the points \( (1, -5) \) and \( (-2, 4) \), the slope is: \[ m = \frac{4 - (-5)}{-2 - 1} = \frac{9}{-3} = -3. \] Now, using the point \( (1, -5) \) and the slope \( m = -3 \), the equation of the line is: \[ y - (-5) = -3(x - 1), \] \[ y + 5 = -3x + 3, \] \[ 3x + y + 2 = 0. \]