To find the slope of the line that contains the given points, we will use the formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's select the first pair of points from the table provided: [tex]\((-1, 10)\)[/tex] and [tex]\((0, 18)\)[/tex].
1. Identify the coordinates of the first point:
- [tex]\(x_1 = -1\)[/tex]
- [tex]\(y_1 = 10\)[/tex]
2. Identify the coordinates of the second point:
- [tex]\(x_2 = 0\)[/tex]
- [tex]\(y_2 = 18\)[/tex]
3. Substitute these values into the slope formula:
[tex]\[
m = \frac{18 - 10}{0 - (-1)}
\][/tex]
4. Calculate the numerator [tex]\( y_2 - y_1 \)[/tex]:
[tex]\[
18 - 10 = 8
\][/tex]
5. Calculate the denominator [tex]\( x_2 - x_1 \)[/tex]:
[tex]\[
0 - (-1) = 0 + 1 = 1
\][/tex]
6. Divide the numerator by the denominator to find the slope:
[tex]\[
m = \frac{8}{1} = 8
\][/tex]
Therefore, the slope of the line that contains the given points is:
[tex]\[
\boxed{8}
\][/tex]
