WHAT IS THE LINEAR EQUATION FOR SCORES ON AN ACHIEVEMENT TEST?

Question

SCORES ON AN ACHIEVEMENT TEST (A) ARE RELATED LINERLY TO SCORES ON ANOTHER TEST (B). HERE ARE THE 2 STUDENTS SCORES A=500, B=100, A=680, B=127

USE THE ORDERED PAIRS (A,B)

USE THE LINEAR EQUATION TO PREDICT THE SCORE ON THE B TEST FOR A STUDENT WITH A SCORE OF 700 ON THE A TEST.

Answer 1

We have two points on a linear scale: (500,100) and (680,127).

From these we can find the slope of the linear relationship:

(127-100)/(680-500)=27/180=3/20.

Now we can plug in either point to find the linear equation:

B-100=(3/20)(A-500)=3A/20-75, B=3A/20+25; or:

B-127=(3/20)(A-680)=3A/20-102, B=3A/20+25 or B=(3A+500)/20.

This can be written in different ways:

20B-3A=500, 3A-20B+500=0, etc.