To determine the slope of the line containing the given points, we follow these steps:
1. Identify the coordinates of the first and the last points:
- The first point [tex]\((x_1, y_1)\)[/tex] is [tex]\((12, -4)\)[/tex].
- The last point [tex]\((x_2, y_2)\)[/tex] is [tex]\((15, 14)\)[/tex].
2. Calculate the change in [tex]\(y\)[/tex] (often called [tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = 14 - (-4) = 14 + 4 = 18
\][/tex]
3. Calculate the change in [tex]\(x\)[/tex] (often called [tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = 15 - 12 = 3
\][/tex]
4. Calculate the slope [tex]\(m\)[/tex] using the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{18}{3} = 6.0
\][/tex]
Therefore, the slope of the line that contains these points is [tex]\(6.0\)[/tex].
