To determine the slope of the line passing through the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\( J \)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\( K \)[/tex].
Given:
[tex]\( (x_1, y_1) = (1, -4) \)[/tex]
[tex]\( (x_2, y_2) = (-2, 8) \)[/tex]
Now, substitute these values into the formula:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]
Simplify the numerator and the denominator:
[tex]\[ m = \frac{8 + 4}{-2 - 1} \][/tex]
[tex]\[ m = \frac{12}{-3} \][/tex]
Perform the division:
[tex]\[ m = -4 \][/tex]
Thus, the slope of the line [tex]\( \overleftrightarrow{ JK } \)[/tex] is [tex]\(-4\)[/tex].
The correct answer is:
A. [tex]\(-4\)[/tex]
