To find the slope of a line that contains the points [tex]\((-1, 9)\)[/tex] and [tex]\( (5, 21) \)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points are [tex]\((-1, 9)\)[/tex] and [tex]\((5, 21)\)[/tex]:
- [tex]\( x_1 = -1 \)[/tex]
- [tex]\( y_1 = 9 \)[/tex]
- [tex]\( x_2 = 5 \)[/tex]
- [tex]\( y_2 = 21 \)[/tex]
Substitute these values into the slope formula:
[tex]\[ \text{slope} = \frac{21 - 9}{5 - (-1)} \][/tex]
Simplify the calculations:
[tex]\[ \text{slope} = \frac{21 - 9}{5 + 1} \][/tex]
[tex]\[ \text{slope} = \frac{12}{6} \][/tex]
[tex]\[ \text{slope} = 2 \][/tex]
Thus, the slope of the line that contains the points [tex]\((-1, 9)\)[/tex] and [tex]\((5, 21)\)[/tex] is [tex]\(2\)[/tex].
So, the correct answer is:
C. [tex]\(2\)[/tex]
