Definition: Linear Equation

A linear equation is an algebraic equation where each term has an exponent of 1. When graphed, it always produces a straight line, which is called a 'linear' equation.

The general form of a linear equation is: ax + by = c.

Explanation:

Here, the given image shows that x and y are variables. The constants a and b represent the coefficients of the variables x and y, respectively, while c is the constant term.

Definition: Linear Functions

A linear function is a mathematical function that can be represented by a straight line when graphed on a Cartesian coordinate system. It takes the form of an algebraic expression.

The general form of a linear function is: f(x) = mx + b.

Explanation:

The given image shows the linear function, so here
f(x) represents the output or dependent variable.
x represents the input or independent variable.
m represents the slope of the line.
b represents the y-intercept (The point where the line crosses the y-axis).

Definition: Linear Inequalities

Linear inequalities are mathematical statements that express a relationship between two algebraic expressions using inequality symbols (<, >, ≤, or ≥). These inequalities involve linear equations, which consist of variables raised to the first power, multiplied or divided by constants.

The general form of a linear inequality is: ax + b < c.

Explanation:

The given image illustrates the inequality ax + b < c, where x is the variable, and a, b, and c are constants.