What is a linear function?

A linear function is a mathematical function that produces a graph of a straight line when plotted on a coordinate plane. Such a function can be described by an equation in the form:

y = mx + b

In this equation:

- y represents the dependent variable (the output of the function). - x represents the independent variable (the input of the function). - m is the slope of the line, which tells you how steep the line is. A positive slope means the line is ascending (going up), while a negative slope means the line is descending (going down). - b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero. The defining attribute of a linear function is that the rate of change is constant. This means that the slope (m) is the same between any two points on the line. Hence, when you increase the independent variable (x) by one unit, the dependent variable (y) will always increase by the same amount (the slope m).

Linear functions can be used to model real-world situations with a constant rate of change, such as predicting profits from sales if the profit per unit is fixed, or converting temperatures between Fahrenheit and Celsius.