To determine the slope of the line that passes through the points [tex]\((-1, 2)\)[/tex] and [tex]\( (3, 3) \)[/tex], we use the slope formula:
[tex]\[
\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Given the points [tex]\((-1, 2)\)[/tex] and [tex]\( (3, 3)\)[/tex]:
- [tex]\( x_1 = -1 \)[/tex]
- [tex]\( y_1 = 2 \)[/tex]
- [tex]\( x_2 = 3 \)[/tex]
- [tex]\( y_2 = 3 \)[/tex]
Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{{3 - 2}}{{3 - (-1)}} = \frac{{3 - 2}}{{3 + 1}} = \frac{1}{4}
\][/tex]
Thus, the slope of the line that contains the points [tex]\((-1, 2)\)[/tex] and [tex]\( (3, 3) \)[/tex] is:
A. [tex]\(\frac{1}{4}\)[/tex]
