Linear Function

A linear function is a type of function in mathematics that can be represented by a straight line when graphed on a coordinate plane. The general form of a linear function is given by the equation 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, and the y-intercept is the point where the line crosses the y-axis.

Key Concepts:

1. Slope: The slope of a linear function is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
2. Y-Intercept: The y-intercept of a linear function is the value of y when x = 0, and it is the point where the line crosses the y-axis.
3. Graphing Linear Functions: Plotting points and using the slope and y-intercept to draw the line on a coordinate plane.
4. Equation of a Line: The equation y = mx + b is the standard form of a linear function, where "m" is the slope and "b" is the y-intercept.
5. Rate of Change: The slope of a linear function represents the rate at which the dependent variable (y) changes with respect to the independent variable (x).

Study Guide:

1. Understand the concept of slope and how it relates to the steepness of a line.
2. Practice finding the y-intercept of a linear function and understand its significance in graphing.
3. Learn to graph linear functions by plotting points and using the slope and y-intercept.
4. Practice converting linear equations between standard form and slope-intercept form (y = mx + b).
5. Understand how to interpret the slope as a rate of change in real-world scenarios.

Understanding linear functions is crucial in algebra and lays the groundwork for more advanced topics in mathematics such as systems of linear equations, slope-intercept form, and linear inequalities.

Good luck with your studies!