Linear functions are mathematical expressions that create straight lines when graphed, characterized by a constant rate of change or slope. They are foundational in understanding relationships between variables in algebra and are represented in the form y = mx + b, where m is the slope and b is the y-intercept.

Linear Functions

Linear functions

Mathematical expressions are combinations of numbers, variables, and operators that represent a specific value or set of values. They are fundamental in mathematics as they allow for the representation and manipulation of mathematical ideas and relationships in a precise and concise manner.

mathematical expressions

straight lines

The rate of change quantifies how one quantity changes in relation to another, often represented as a derivative in calculus. It is a fundamental concept in mathematics and science, used to understand dynamic systems and model real-world phenomena.

rate of change

The slope of a line in a two-dimensional space represents the rate of change of the dependent variable as the independent variable changes, often visualized as the 'steepness' of the line. It is calculated as the ratio of the vertical change to the horizontal change between two points on the line, commonly referred to as 'rise over run'.

slope

Sometimes, things can change together, like how when it gets colder, we wear more clothes. We call these things 'variables', and when one changes, it might make another change too.

relationships between variables

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols to solve equations and understand relationships between quantities. It serves as a unifying thread of almost all mathematics, providing a foundation for advanced studies in various scientific and engineering disciplines.

algebra

y = mx + b

The y-intercept of a function is the point where its graph intersects the y-axis, representing the value of the function when the input is zero. It is a fundamental concept in linear equations and can be found by setting the independent variable to zero in the equation of the line or curve.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

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