Final answer:
To predict the value of variable J when variable K equals 12, we can use the trend line equation. By finding the slope and y-intercept, we can determine the equation of the trend line. Substituting K = 12 into the equation gives the predicted value of J as 44.
Step-by-step explanation:
To predict the value of variable J when variable K equals 12, we can use the trend line. Based on the given data, we can determine the equation of the trend line by finding the slope and the y-intercept. Once we have the equation, we can substitute K = 12 into the equation to find the predicted value of J.
Given data:
K: 10, 12, 14
J: 32, ?, ?
The equation of the trend line can be determined using the first and last data points:
Slope: (J2 - J1) / (K2 - K1) = (32 - J1) / (14 - 10) = 6
Using the slope and one of the data points, we can find the y-intercept:
J1 = 32 - (slope * K1) = 32 - (6 * 10) = -28
So, the equation of the trend line is J = 6K - 28. Now, substitute K = 12 into the equation to find J:
J = 6(12) - 28 = 72 - 28 = 44
Therefore, when K equals 12, the predicted value of J is 44.