To identify the slope and the coordinates of a point on the line given by the point-slope form equation \( y - 4 = \frac{1}{2}(x - 1) \), we can proceed as follows:
1. Identify the Slope:
The point-slope form of a linear equation is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.
Comparing the given equation \( y - 4 = \frac{1}{2}(x - 1) \) with the point-slope form:
[tex]\[
y - 4 = \frac{1}{2}(x - 1)
\][/tex]
we can see that the slope \(m\) is \(\frac{1}{2}\).
Therefore, the slope of the line is \(\boxed{0.5}\).
2. Identify a Point on the Line:
From the point-slope form, the coordinates \( (x_1, y_1) \) are taken directly from the equation. Here, we have:
[tex]\[
y - 4 = \frac{1}{2}(x - 1)
\][/tex]
By comparing this with the generic formula:
[tex]\[
y - y_1 = m(x - x_1),
\][/tex]
we can identify that:
[tex]\[ y_1 = 4 \][/tex]
[tex]\[ x_1 = 1 \][/tex]
Thus, a point on the line is \((1, 4)\).
Therefore, a point on the line is \(\boxed{(1, 4)}\).
In summary:
- The slope of the line is \(\boxed{0.5}\).
- A point on the line is [tex]\(\boxed{(1, 4)}\)[/tex].
