Question

If the slope of the straight line joining the points \((2,3)\) and \((5,7)\) is \(m\), then \(9m^2=\)

• A. 1
• B. 4
• C. 9
• D. 16

Hint:

Slope formula: \[ \boxed{m=\frac{y_2-y_1}{x_2-x_1}} \] Always subtract the coordinates in the same order.

Answer 1

The Correct Option is D

Concept: The slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \[ \boxed{m=\frac{y_2-y_1}{x_2-x_1}}. \]

Step 1: Find the slope.
Given points are \[ (2,3)\quad\text{and}\quad(5,7). \] Therefore, \[ m=\frac{7-3}{5-2} =\frac43. \]

Step 2: Find \(9m^2\).
\[ 9m^2 =9\left(\frac43\right)^2 =9\cdot\frac{16}{9} =16. \]

Step 3: Final conclusion.
Hence, \[ \boxed{9m^2=16.} \]