functionslinear

A linear function is a mathematical function that can be represented by a straight line on a graph. Its general form is often written as y = mx + b, where 'y' is the dependent variable, 'x' is the independent variable, 'm' represents the slope of the line, and 'b' is the y-intercept. The slope 'm' indicates how steep the line is and in which direction it rises or falls. A positive slope means the line goes upward from left to right, while a negative slope means it goes downward. The y-intercept 'b' is the point where the line crosses the y-axis. Linear functions are characterized by a constant rate of change. This means that for every unit increase in the independent variable 'x', the dependent variable 'y' changes by a fixed amount, which is the slope 'm'. They are fundamental in algebra and have numerous applications in science, engineering, economics, and everyday life, such as modeling constant speeds, simple interest calculations, and proportional relationships.