A linear equation is a mathematical statement that describes a straight line when graphed on a coordinate plane, typically in the form of y = mx + b where m is the slope and b is the y-intercept. It represents a constant rate of change and is foundational in algebra for modeling relationships with constant proportionality.

Linear Equation

linear equation

straight line

A coordinate plane is a two-dimensional surface on which points are plotted and defined by a pair of numerical coordinates, typically represented as (x, y). It serves as a fundamental tool in mathematics for graphing equations, understanding geometric concepts, and analyzing data relationships.

coordinate plane

y = mx + b

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

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.

y-intercept

constant rate of change

foundational in algebra

modeling relationships

constant proportionality

Breaking Down the Equation y = mx + b

Exploring the Linear Equation: y = mx + b

The Slope of Your Motivation: Understanding the Gradient of a Line

Understanding Slope

Exploring Positive Slope in Slope Calculation

Slope-Intercept Form

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