To find the slope of the line passing through the two points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], follow these steps:
1. Identify the coordinates of the two points:
- [tex]\( J(1, -4) \)[/tex]
- [tex]\( K(-2, 8) \)[/tex]
2. Recall the slope formula:
The slope [tex]\( m \)[/tex] between 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:
- Here, [tex]\( x_1 = 1 \)[/tex], [tex]\( y_1 = -4 \)[/tex], [tex]\( x_2 = -2 \)[/tex], and [tex]\( y_2 = 8 \)[/tex].
4. Calculate the difference in the y-coordinates (rise):
[tex]\[
y_2 - y_1 = 8 - (-4) = 8 + 4 = 12
\][/tex]
5. Calculate the difference in the x-coordinates (run):
[tex]\[
x_2 - x_1 = -2 - 1 = -3
\][/tex]
6. Find the slope by dividing the rise by the run:
[tex]\[
m = \frac{12}{-3} = -4
\][/tex]
Therefore, the slope of the line [tex]\(\overleftrightarrow{JK}\)[/tex] is [tex]\(-4\)[/tex].
So, the correct answer is:
A. -4
