To determine the slope of the line passing through the points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex], we can use the formula for the slope of a line given two points:
[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].
1. Identify the coordinates of the points [tex]\( J \)[/tex] and [tex]\( K \)[/tex]:
- [tex]\( J(x_1, y_1) = (-1, -9) \)[/tex]
- [tex]\( K(x_2, y_2) = (5, 3) \)[/tex]
2. Substitute these values into the slope formula:
[tex]\[ m = \frac{3 - (-9)}{5 - (-1)} \][/tex]
3. Simplify the numerator and the denominator:
- The numerator [tex]\( y_2 - y_1 = 3 - (-9) = 3 + 9 = 12 \)[/tex]
- The denominator [tex]\( x_2 - x_1 = 5 - (-1) = 5 + 1 = 6 \)[/tex]
4. Calculate the slope:
[tex]\[ m = \frac{12}{6} = 2 \][/tex]
Therefore, the slope of the line passing through the points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\( 2 \)[/tex].
The correct answer is:
D. 2
