To find the slope of the line that passes through the points [tex]\((-1, -4)\)[/tex] and [tex]\((-2, 1)\)[/tex], follow these steps:
1. Identify the coordinates of the two points. Let's denote [tex]\((-1, -4)\)[/tex] as [tex]\((x_1, y_1)\)[/tex] and [tex]\((-2, 1)\)[/tex] as [tex]\((x_2, y_2)\)[/tex].
- [tex]\(x_1 = -1\)[/tex]
- [tex]\(y_1 = -4\)[/tex]
- [tex]\(x_2 = -2\)[/tex]
- [tex]\(y_2 = 1\)[/tex]
2. Calculate the change in [tex]\(y\)[/tex], known as [tex]\(\Delta y\)[/tex]:
[tex]\[
\Delta y = y_2 - y_1
\][/tex]
Substituting the given values:
[tex]\[
\Delta y = 1 - (-4) = 1 + 4 = 5
\][/tex]
3. Calculate the change in [tex]\(x\)[/tex], known as [tex]\(\Delta x\)[/tex]:
[tex]\[
\Delta x = x_2 - x_1
\][/tex]
Substituting the given values:
[tex]\[
\Delta x = -2 - (-1) = -2 + 1 = -1
\][/tex]
4. Check if the line is vertical. A line is vertical if [tex]\(\Delta x = 0\)[/tex]. Here, [tex]\(\Delta x \neq 0\)[/tex], so the slope is defined.
5. Compute the slope [tex]\(m\)[/tex] using the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
Substituting the calculated values:
[tex]\[
m = \frac{5}{-1} = -5
\][/tex]
So, the slope of the line that passes through the points [tex]\((-1, -4)\)[/tex] and [tex]\((-2, 1)\)[/tex] is:
[tex]\[
\boxed{-5}
\][/tex]
