To determine the slope of the line that passes through the points [tex]\((-1, 2)\)[/tex] and [tex]\( (4, 3) \)[/tex], we can use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Now let's identify our points:
- [tex]\((x_1, y_1) = (-1, 2)\)[/tex]
- [tex]\((x_2, y_2) = (4, 3)\)[/tex]
Plug these values into the slope formula:
[tex]\[
\text{slope} = \frac{3 - 2}{4 - (-1)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{1}{4 + 1}
\][/tex]
[tex]\[
\text{slope} = \frac{1}{5}
\][/tex]
Therefore, the slope of the line that contains the points [tex]\((-1, 2)\)[/tex] and [tex]\( (4, 3) \)[/tex] is [tex]\(\frac{1}{5}\)[/tex], which corresponds to option C.
So, the correct answer is:
C. [tex]\(\frac{1}{5}\)[/tex]
