Sure! Let's analyze the point-slope form equation given: [tex]\( y - 4 = \frac{1}{2}(x - 1) \)[/tex].
The point-slope form of a line is generally written as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( m \)[/tex] is the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is a specific point on the line.
1. Identifying the Slope:
- The formula shows that [tex]\( m \)[/tex], the slope, is the coefficient of the term [tex]\((x - x_1)\)[/tex].
- From [tex]\( y - 4 = \frac{1}{2}(x - 1) \)[/tex], we see that the slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{0.5} \][/tex]
2. Identifying a Point on the Line:
- The formula also shows that [tex]\((x_1, y_1)\)[/tex] is the point from which the line is described.
- From [tex]\( y - 4 = \frac{1}{2}(x - 1) \)[/tex], we can see the terms [tex]\((x_1, y_1)\)[/tex]. Here, [tex]\( x_1 = 1 \)[/tex] and [tex]\( y_1 = 4 \)[/tex].
Therefore, a point on the line is:
[tex]\[ (1, 4) \][/tex]
So, summarizing:
- The slope of the line is [tex]\( \boxed{0.5} \)[/tex]
- A point on the line is [tex]\( \boxed{(1, 4)} \)[/tex]
