Question

If the slope of the line through (x, 5) and (5, 2) is 3, then the value of x is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The Correct Option is D

To solve the problem, we need to determine the value of \( x \) such that the slope of the line passing through the points \( (x, 5) \) and \( (5, 2) \) is 3.

1. Formula for Slope:
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In this problem, the points are \( (x, 5) \) and \( (5, 2) \), and the slope \( m \) is given as 3. Substituting these values into the formula:

\[ 3 = \frac{2 - 5}{5 - x} \]

2. Simplifying the Equation:
Simplify the numerator on the right-hand side:

\[ 3 = \frac{-3}{5 - x} \]

3. Solving for \( x \):
To isolate \( x \), multiply both sides of the equation by \( 5 - x \):

\[ 3(5 - x) = -3 \]

Distribute the 3 on the left-hand side:

\[ 15 - 3x = -3 \]

Subtract 15 from both sides:

\[ -3x = -3 - 15 \] \[ -3x = -18 \]

Divide both sides by \(-3\):

\[ x = \frac{-18}{-3} = 6 \]

4. Verifying the Solution:
To ensure correctness, substitute \( x = 6 \) back into the slope formula:

\[ m = \frac{2 - 5}{5 - 6} = \frac{-3}{-1} = 3 \]

This confirms that the slope is indeed 3.

Final Answer:
The value of \( x \) is \( {6} \).