Final answer:
To find the slope of line k, which is perpendicular to line j, we can use the fact that the product of the slopes of two perpendicular lines is -1. The slope of line j can be found using the formula for slope, and then the slope of line k can be found by taking the negative reciprocal of the slope of line j.
Step-by-step explanation:
In order to find the slope of line k, which is perpendicular to line j, we can use the fact that the product of the slopes of two perpendicular lines is -1. The slope of line j can be found by using the formula:
slope = (change in y) / (change in x)
Given the points (3, 13) and (8, 9), we can use these values to find the slope of line j. Then, we can find the slope of line k by taking the negative reciprocal of the slope of line j.
Using the formula for slope, we have:
slope of line j = (9 - 13) / (8 - 3) = -4 / 5
The slope of line k is the negative reciprocal of the slope of line j, so:
slope of line k = -1 / (-4 / 5) = 5 / 4.