Simple Linear Equations - SS2 Economics Lesson Note

Simple linear equations are mathematical expressions that involve a single variable, which is usually represented by the letter "x". The general form of a simple linear equation is:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. The slope of the line represents the rate of change of the dependent variable with respect to the independent variable, while the y-intercept represents the value of the dependent variable when the independent variable is zero.

To solve a simple linear equation, we need to isolate the variable x on one side of the equation. For example, given the equation:

2x + 3 = 7

we can solve for x by subtracting 3 from both sides of the equation:

2x = 4

and then dividing both sides by 2:

x = 2

Therefore, the solution to the equation is x = 2.

Simple linear equations are used to model many real-world situations. They are also the basis for more complex equations and models used in fields such as economics. In economics, simple linear equations are often used to model the relationship between two economic variables. For example, the demand for a product may be related to its price, or the quantity of a product supplied may be related to its price.

A simple linear equation that models the relationship between the quantity demanded of a product and its price may take the form:

Qd = a - bP

where Qd is the quantity demanded, P is the price of the product, a is the intercept of the equation (the quantity demanded when the price is zero), and b is the slope of the equation (the change in quantity demanded for a one-unit change in price).

This equation tells us that as the price of a product increases, the quantity demanded of the product decreases (assuming everything else remains constant). Conversely, as the price of a product decreases, the quantity demanded of the product increases

Simple linear equations like this one are used to estimate demand curves and supply curves, which are important tools in microeconomics. They help businesses and policymakers make decisions about pricing, production, and allocation of resources.