Topic 3: Linear Functions (enVision Algebra 1)

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

The slope (m) represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

The y-intercept (b) is the point where the graph of the function crosses the y-axis. It represents the value of f(x) when x = 0.

A vertical translation shifts the graph up or down. If k is positive, the graph shifts up; if k is negative, it shifts down.

A horizontal translation shifts the graph left or right. If h is positive, the graph shifts left; if h is negative, it shifts right.

To evaluate a linear function f(x) at a specific point x = a, substitute a into the function and calculate f(a).

The line of best fit can be found using linear regression, which calculates the best-fitting line through a set of data points.

A correlation coefficient of 0.99 indicates a very strong positive linear relationship between two variables.

The slope of the line of best fit indicates the average change in the dependent variable for each unit increase in the independent variable.

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.