To determine the slope of the given line from the point-slope form of the equation, let's start by understanding the point-slope form itself.
The point-slope form of a linear equation is expressed as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.
Given the equation:
[tex]\[ y - 9 = \frac{1}{5}(x - 2) \][/tex]
We can compare this to the standard point-slope form:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
From the comparison:
- [tex]\(y_1 = 9\)[/tex]
- [tex]\(x_1 = 2\)[/tex]
- [tex]\(m = \frac{1}{5}\)[/tex]
The slope [tex]\(m\)[/tex] of the line is [tex]\(\frac{1}{5}\)[/tex].
Therefore, the correct answer is:
D. [tex]\(\frac{1}{5}\)[/tex]
