2. persons with a low sense of humor have higher levels of depression in response to negative life events
than those with a high sense of humor. the low-humor group is modeled by d =
10
9
x +
53
9
and the
high-humor group is modeled by d =
1
9
x +
26
9
. the variable x represents the intensity of a negative life
event (from 1, low, to 10, high) and d is the average level of depression in response to that event. if the
high-humor group averages a level of depression of 2.5 in response to a negative life event, what is the
intensity of that event?

The two models given are:

Low sense of humor:

D = [10/9]x + 53/9

High sense of humor:

D = [1/9]x + 26/9

Now you are told to use the high-humor model to find the intensity (x) of an event that causes a depression (D) level of 2.5.

Then you have to reverse the equation, this is to solve for x

Step 1: subtract 26/9 from both sides =>

D - 26/9 = [1/9]x

Step 2: multiply both sides times 9 =>

9[D - 26/9] = x

=> x = 9D - 26

Now you use D value to find x value:

D = 2.5 => X =9(2.5) - 26 = 22.5 - 26 = - 3.5

You got a negative value of D.

This is an unfortunate model and should not have been chosen, because the model is for D between 1 and 10, then the negative result is contradictory.

But the important thing is that you understand the idea that a the equations are used to represent models and you can work them algebraically.