Find the slope of a line, which passes through the origin, and the midpoint of the line segment joining the points `P (0, 4)`and `B (8, 0)`.

Explanation

To find the slope of the line that passes through the origin and the midpoint of the line segment joining the points \( P(0, 4) \) and \( B(8, 0) \), we can follow these steps:

### Step 1: Find the Midpoint of the Line Segment
The formula for finding the midpoint \( M \) of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, the coordinates of point \( P \) are \( (0, 4) \) and the coordinates of point \( B \) are \( (8, 0) \).

Substituting the values into the midpoint formula:
\[ M = \left( \frac{0 + 8}{2}, \frac{4 + 0}{2} \right) = \left( \frac{8}{2}, \frac{4}{2} \right) = (4, 2) \]

### Step 2: Use the Slope Formula
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, we have the origin \( (0, 0) \) as one point and the midpoint \( (4, 2) \) as the other point.

Let \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (4, 2) \).

Substituting these values into the slope formula:
\[ m = \frac{2 - 0}{4 - 0} = \frac{2}{4} = \frac{1}{2} \]

### Final Answer
The slope of the line is \( \frac{1}{2} \).

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