The equation you've provided:

\[
y - 0 = \frac{1}{2}(x - 4)
\]

is in **point-slope form** of a linear equation, where:

\[
y - y_1 = m(x - x_1)
\]

Here, \( m = \frac{1}{2} \) is the slope of the line, and \( (x_1, y_1) = (4, 0) \) is the point through which the line passes.

### Simplifying the equation:
\[
y = \frac{1}{2}(x - 4)
\]

Next, distribute the \(\frac{1}{2}\) across the terms inside the parentheses:
\[
y = \frac{1}{2}x - \frac{1}{2}(4)
\]
\[
y = \frac{1}{2}x - 2
\]

So, the equation of the line in **slope-intercept form** is:
\[
y = \frac{1}{2}x - 2
\]

### Summary:
- The slope (\(m\)) is \(\frac{1}{2}\).
- The y-intercept is \(-2\).
- The line passes through the point \((4, 0)\).

Would you like more details or have any questions?

### Related Questions:
1. How can we find the slope of a line passing through two points?
2. What is the general form of a linear equation?
3. How do we convert slope-intercept form back to point-slope form?
4. What are the differences between point-slope form and slope-intercept form?
5. How do we calculate the equation of a line parallel to a given line?

### Tip:
The point-slope form is very useful when you know a point on the line and the slope, but need the equation.

Learn how to convert the linear equation y - 0 = (1/2)(x - 4) from point-slope form to slope-intercept form. This problem covers key algebraic concepts such as slope, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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