Transcript Linear Project Modeling Algebra Section 7

SOURCE: NATIONAL
HOUSEHOLD SURVEY ON DRUG
ABUSE
HTTP://WWW.OAS.SAMHSA.GOV/2K8/YOUTHDEPRESS/YOUTHDEPRESS.HTM
Percentages of Youths Aged 12 to 16 Who Experienced a
Past Year Major Depressive Episode (MDE), by Age: 20042006
PERCENTAGE OF YOUTHS AGES 12 TO 16 WHO
EXPERIENCED MAJOR DEPRESSIVE EPISODE
11.5
11.1
PERCENTAGE
10.1
9.7
9.1
8.1
7.9
7.1
6.2
6.1
5.1
4.1
4.1
12
13
14
AGE OF YOUTHS
15
16
Pick two points from data (12, 4.1) (13, 6.2)
Y -Y
 Use Slope Formula m= 1 2
X -X

1


2
Plug in points: (4.1-6.2) / (12-13)= -2.1/-1= 2.1
Plug in slope and choose one set of points to plug
into y-intercept formula: y=mx+b and solve for
b
(4.1)= 2.1(12) + b
 Multiply 2.1 12= 25.2
 Subtract 4.1
25.2= therefore b= -21.1


FORMULA: Y=
2.1x- 21.1
FOR EVERY AGE INCREASE AN
ADDITIONAL 2.1 YOUTHS EXPERIENCE A
MAJOR DEPRESSIVE EPISODE
FINDING VERTICAL INTERCEPT
Y= 2.1x-22.1
 PLUG IN ZERO FOR X
 Y=2.1(0)-22.1
 Y= -22.1

 Therefore
when a child is born the percentage of a depressive
episode is -22.1% According to our model this means when a
child is born there is a negative percent of a child being born
depressed.

Yes, this equation models the situation near the intercepts
FINDING HORIZONTAL INTERCEPT
Y= 2.1x- 22.1
 Plug in zero for Y
 (0)= 2.1x- 22.1
 22.1= 2.1x
 Divide 22.1 by 2.1
 X= 10.5

 Therefore
when a child is 10 and a half they will have a 0%
chance of having a depressive episode according to the
model.

Yes, this equation models the situation near the intercepts
GRAPH CONTAINING SCATTER PLOT
AND EQUATION Y= 2.1X- 22.1
11.5
11.1
PERCENTAGE
10.1
9.7
9.1
8.1
7.9
7.1
6.2
6.1
5.1
4.1
4.1
12
13
14
AGE OF YOUTHS
15
16
The model can be used to see when teens and
individuals in their early twenties are most likely
to have a higher percentage of a major depressive
episode
 Age 18: y= 2.1(18) – 22.1= 15.7%
 Age 21: y= 2.1(21) – 22.1= 22%
