To determine the slope of the line that contains the points [tex]\((-1, 9)\)[/tex] and [tex]\((5, 21)\)[/tex], you can follow these steps:
1. Identify the coordinates of the points:
- The first point [tex]\((x_1, y_1)\)[/tex] is [tex]\((-1, 9)\)[/tex].
- The second point [tex]\((x_2, y_2)\)[/tex] is [tex]\((5, 21)\)[/tex].
2. Recall the slope formula:
The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Substitute the coordinates into the formula:
[tex]\[
m = \frac{21 - 9}{5 - (-1)}
\][/tex]
4. Simplify the expression:
[tex]\[
m = \frac{21 - 9}{5 + 1}
\][/tex]
[tex]\[
m = \frac{12}{6}
\][/tex]
5. Calculate the slope:
[tex]\[
m = \frac{12}{6} = 2
\][/tex]
Thus, the slope of the line that contains the points [tex]\((-1, 9)\)[/tex] and [tex]\((5, 21)\)[/tex] is 2.
The correct answer is:
C. 2
