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To solve this problem, we can determine the equation of a line using the given intercepts:

- The **x-intercept** is 8, meaning the point \((8, 0)\) lies on the line.
- The **y-intercept** is 4, meaning the point \((0, 4)\) lies on the line.

The equation of a line in **slope-intercept form** is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope
- \(b\) is the y-intercept (which is already given as 4)

### Step 1: Calculate the slope
The slope \(m\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((8, 0)\) and \((0, 4)\):

\[
m = \frac{4 - 0}{0 - 8} = \frac{4}{-8} = -\frac{1}{2}
\]

### Step 2: Write the equation
Now that we know the slope \(m = -\frac{1}{2}\) and the y-intercept is 4, we can write the equation as:

\[
y = -\frac{1}{2}x + 4
\]

### Step 3: Match with the given options
This matches **Option C**, which is:

\[
y = -\frac{1}{2}x + 4
\]

Thus, the correct answer is **C**.

Would you like further explanation on any part? Here are five related questions to deepen your understanding:

1. How do you find the slope of a line given two points?
2. Can you derive the equation of a line if only one point and the slope are given?
3. What is the significance of the y-intercept in the slope-intercept form?
4. How can we find the x-intercept of a line if only the equation is given?
5. How does the sign of the slope affect the graph of the line?

**Tip:** When finding the slope, always ensure to subtract the coordinates in the same order (e.g., \(y_2 - y_1\) and \(x_2 - x_1\)).

The x-intercept of a line is 8 and its y-intercept is 4. Which equation represents the line?

Learn how to find the equation of a line given its x-intercept at 8 and y-intercept at 4. This problem covers the slope-intercept form and the formula for slope calculation. Suitable for students in Grades 8-10.

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