Question

If the slope of the line joining the two points P(2,5) and Q(x, 3) is 2, then the value of x is

• A. 1
• B. 2
• C. -2
• D. -1

Answer 1

The Correct Option is A

The formula for the slope of the line joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}. \] For the points \( P(2, 5) \) and \( Q(x, 3) \), the slope is given as 2. Therefore, we can use the formula: \[ \frac{3 - 5}{x - 2} = 2. \] Simplifying the left-hand side: \[ \frac{-2}{x - 2} = 2. \] Now, multiply both sides by \( x - 2 \): \[ -2 = 2(x - 2). \] Expanding the right-hand side: \[ -2 = 2x - 4. \] Solving for \( x \): \[ 2x = 2 \quad \Rightarrow \quad x = 1. \]

The correct option is (A): \(1\)