Question

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

• A. \( \frac{x-3}{3} = \frac{y-4}{-5} = \frac{z+7}{8} \)
• B. \( \frac{x-3}{3} = \frac{y-4}{5} = \frac{z+7}{8} \)
• C. \( \frac{x-3}{-3} = \frac{y-4}{-5} = \frac{z+7}{8} \)
• D. \( \frac{x-3}{3} = \frac{y-4}{-5} = \frac{z-7}{8} \)

Hint:

When finding the equation of a line through two points, use the parametric form and substitute the coordinates directly.

Answer 1

The Correct Option is A

Step 1: Equation of the line.
The equation of a line passing through two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by the parametric form: \[ \frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} = \frac{z - z_1}{z_2 - z_1} \] Step 2: Substitute the values.
Substituting the points \( (3, 4, -7) \) and \( (6, -1, 1) \), we get: \[ \frac{x - 3}{6 - 3} = \frac{y - 4}{-1 - 4} = \frac{z + 7}{1 + 7} \] Simplifying: \[ \frac{x - 3}{3} = \frac{y - 4}{-5} = \frac{z + 7}{8} \] Step 3: Conclusion.
Thus, the equation of the line is \( \boxed{\frac{x-3}{3} = \frac{y-4}{-5} = \frac{z+7}{8}} \).