# 30MSC 2023 #28: Specific and General

We often generalize from specific observations. We study the relations of numbers in sequences and formulate general rules to describe the pattern and later use those rules to get specific values for certain terms in the sequence.

Algebra is a generalization of specific arithmeticprocedures and is used generate specific values.

In Vedic Math, there are specific procedures for multiplying numbers near bases and also for numbers that have identical initial digits and the last digits adding up to 10, but also have the vertically and crosswise general method.

Our problem for today, which was taken from the Senior IVMO 2023, is the a very good application of the Specific and General sutra: What is the equation for the straight line with gradient 2/3 and which passes through the point (6, -2)?

The general equation of a line with gradient 2/3 is y = 2x/3 + c

The specific value of c for the line with gradient 2/3 and passing thru (6, 2) is;

-2 = 2(6)/3 + c

-2 = 4 + c

c = – 6

Therefore, the equation of the required line is

y =  2x/3 – 6

3y = 2x – 18

Or 2x – 3y = 18

Other applications of the specific and the general are presented in Chapter 8 of our forthcoming book 30 Master Strategies in Computing, Vol III.

Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #29: Triples.