A linear function is a mathematical equation in the form of y = mx + b, where m is the slope and b is the y-intercept. It represents a straight line on a graph and can be used to model relationships between two variables.
The slope of a linear function can be determined by finding the change in y values over the change in x values between any two points on the line. This can be written as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
The y-intercept is the point where the line crosses the y-axis on a graph. In a linear function, it is represented by the value of b in the equation y = mx + b. It indicates the initial value of y when x is equal to 0.
Linear functions can be used to model real-world situations and solve problems by representing the relationship between two variables. For example, they can be used to calculate the total cost of a purchase based on the price per item and quantity bought, or to determine the rate of change of a quantity over time.
One common misconception is that linear functions always have a positive slope. In reality, the slope can be positive, negative, or zero. Another misconception is that the y-intercept represents the starting point of a graph, when in fact it is only the value of y when x is equal to 0. Additionally, linear functions can only model relationships between two variables and cannot account for non-linear relationships.