Final answer:
The slope of LM is 4/5.
Step-by-step explanation:
To find the slope of LM, we first need to find the slope of JK. The slope of a line is determined using the formula: slope = (y2 - y1) / (x2 - x1). For JK, we have the coordinates J (-3, 9) and K (5, -1). So, the slope of JK is (9 - (-1)) / (-3 - 5) = 10 / -8 = -5/4.
Since LM is perpendicular to JK, the slopes of the two lines are negative reciprocals of each other. Therefore, the slope of LM is the negative reciprocal of -5/4, which is 4/5.