Question

Find the equation of the line passing through the two points \( (3, 5) \) and \( (-4, 2) \):

• A. \( 3x - 7y + 26 = 0 \)
• B. \( 3x + 7y + 26 = 0 \)
• C. \( 7x - 3y + 26 = 0 \)
• D. \( 3x - 7y + 62 = 0 \)

Hint:

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

Answer 1

The Correct Option is A

The formula for the equation of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ \frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} \] Substitute the points \( (3, 5) \) and \( (-4, 2) \) into the equation: \[ \frac{x - 3}{-4 - 3} = \frac{y - 5}{2 - 5} \] \[ \frac{x - 3}{-7} = \frac{y - 5}{-3} \] Now, cross-multiply: \[ 3(x - 3) = 7(y - 5) \] Simplifying: \[ 3x - 9 = 7y - 35 \] \[ 3x - 7y = -26 \] Thus, the equation of the line is \( 3x - 7y + 26 = 0 \).