Question

If a line is passing through the points (2, 5) and (x, 3) and its slope is 2. Then the value of 'x' is?

• A. 6
• B. 7
• C. 8
• D. 9

Hint:

To find the slope of a line, always use the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Answer 1

The Correct Option is A

Step 1: Using the formula for the slope of a line. The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Step 2: Substitute the given values.
We are given:
Point 1: \( (x_1, y_1) = (2, 5) \)
Point 2: \( (x_2, y_2) = (x, 3) \)
Slope \( m = 2 \)
Substitute these values into the slope formula: \[ 2 = \frac{3 - 5}{x - 2} \] Simplify the equation: \[ 2 = \frac{-2}{x - 2} \] Multiply both sides by \( (x - 2) \): \[ 2(x - 2) = -2 \] \[ 2x - 4 = -2 \] Solve for \( x \): \[ 2x = 2 \quad \Rightarrow \quad x = 1 \]