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.