What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is a way of expressing a linear relationship between two variables, typically (y) and (x). It is written as (y = mx + b), where (m) represents the slope of the line and (b) indicates the y-intercept, the point at which the line crosses the y-axis.

In this form, the slope (m) is a measure of how steep the line is; it indicates the change in (y) for a one-unit change in (x). The intercept (b) provides a starting value for (y) when (x) is zero.

This format is particularly useful in graphing linear equations because it allows one to quickly identify both the slope and y-intercept, facilitating the drawing of the line on a coordinate plane. Understanding this form is crucial for solving problems involving linear relationships and for further studies in algebra and calculus.