To find the slope of the line passing through two given points, we use the slope formula. For the points \( J(1, -4) \) and \( K(-2, 8) \), the slope \( m \) is calculated as follows:
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \( (x_1, y_1) = J(1, -4) \) and \( (x_2, y_2) = K(-2, 8) \). Substituting these values into the formula, we get:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]
First, compute the numerator:
[tex]\[ 8 - (-4) = 8 + 4 = 12 \][/tex]
Next, compute the denominator:
[tex]\[ -2 - 1 = -3 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ m = \frac{12}{-3} = -4 \][/tex]
Thus, the slope of the line passing through points \( J(1, -4) \) and \( K(-2, 8) \) is \( -4 \).
The correct answer is:
A. -4
