Use the point-slope equation to identify the slope and the coordinates of a point on the line \( y - 4 = \frac{1}{2}(x - 1) \).

The slope of the line is \(\boxed{\frac{1}{2}}\).

A point on the line is [tex]\(\boxed{(1, 4)}\)[/tex].



Answer :

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].