Question

Find the slope of the line passing through the points $ (1, 2) $ and $ (3, 6) $:

• A. 3
• B. 2
• C. 4
• D. 1

Hint:

Key Fact: Slope \( m = \frac{\Delta y}{\Delta x} \)

Answer 1

The Correct Option is B

To find the slope of a line passing through two points, use the formula:

\( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Given points \((1, 2)\) and \((3, 6)\):

• \((x_1, y_1) = (1, 2)\)
• \((x_2, y_2) = (3, 6)\)

Substitute these values into the formula:

\( m = \frac{6 - 2}{3 - 1} \)

\( m = \frac{4}{2} \)

\( m = 2 \)

Thus, the slope of the line is \(2\).

Answer 2

To solve the problem, we need to find the slope of the line passing through the points $(1, 2)$ and $(3, 6)$.

1. Formula for the slope of a line: 
The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$ m = \frac{y_2 - y_1}{x_2 - x_1} $

2. Substitute the given points:
$ x_1 = 1, y_1 = 2 $
$ x_2 = 3, y_2 = 6 $

3. Calculate the slope:
$ m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2 $

Final Answer:
The slope of the line is $ {2} $.