Linear Functions: Definition, Equations, And Applications

Linear (Identity) Function

y = x

A linear function, also called an identity function, is a mathematical equation where the output of the function is directly proportional to the input. In other words, a linear function is a straight line with a constant slope. The general form of a linear function is:

y = mx + b

In this equation, y represents the output or dependent variable, x represents the input or independent variable, m represents the slope or rate of change of the line, and b represents the y-intercept or the point where the line crosses the y-axis.

The slope of a linear function tells us how much the output changes for every unit change in the input. If the slope is positive, the line is slanting upwards from left to right, suggesting that the output variable increases as the input variable increases. If the slope is negative, the line is slanting downwards, suggesting that the output variable decreases as the input variable increases.

The y-intercept of the line tells us the output value when the input value is zero. For example, if the equation of a linear function is y = 2x – 1, the graph of this function will cross the y-axis at point (0, -1), indicating that when the input value is zero, the output value is -1.

Many real-life situations can be modeled using linear functions, such as calculating the total cost of goods produced, determining the distance traveled by an object, or plotting the trend of stock prices over time.

More Answers: