LESSON 2 Writing Rules for Linear Functions

Answer 1

When writing linear functions, there are several key rules to keep in mind:

1. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the function, while the y-intercept is the value of y when x = 0.

2. The slope, m, can be calculated as the change in y divided by the change in x between two points on the line. It can also be identified from the equation of the line by looking at the coefficient of x.

3. The y-intercept, b, is the value of y when x = 0. It can be found by substituting x = 0 into the equation of the line and solving for y.

4. When writing the equation of a linear function, make sure to use proper mathematical notation and symbols. The variable for the independent variable (usually x) should be clearly defined, and the dependent variable (usually y) should be isolated on one side of the equation.

5. When graphing a linear function, plot the y-intercept first, then use the slope to find additional points on the line. Connect the points with a straight line to represent the linear function.

6. When describing the behavior of a linear function, consider how the slope and y-intercept affect the graph and the function itself. A positive slope indicates a line that is increasing, while a negative slope indicates a line that is decreasing. The y-intercept determines where the line intersects the y-axis.

By following these rules and guidelines, you can effectively write, graph, and analyze linear functions in mathematics.