Question

What is the slope of the straight line? I) The straight line passes through the origin and the point \((3,2)\).
II) The straight line passes through \((3,3)\).

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

To find the slope of a line, two distinct points are sufficient. One point alone is not sufficient.

Answer 1

The Correct Option is A

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

Step 1: Check Statement I. The line passes through \[ (0,0) \] and \[ (3,2) \] So the slope is \[ m=\frac{2-0}{3-0} \] \[ m=\frac{2}{3} \] Thus Statement I alone is sufficient.

Step 2: Check Statement II. Statement II says the line passes through only one point: \[ (3,3) \] Infinitely many lines can pass through a single point, and they can have different slopes. Therefore, Statement II alone is not sufficient.

Step 3: Final answer. \[ \boxed{\text{Statement I alone is sufficient}} \]