What is the slope-intercept form of a line?

The slope-intercept form of a line is given by the equation (y = mx + b), where (m) represents the slope of the line and (b) represents the y-intercept. This form is particularly useful because it allows you to easily identify both the rate at which the line rises or falls (the slope) and the point at which the line crosses the y-axis (the y-intercept).

The slope, (m), indicates how much (y) changes for a unit increase in (x). A positive slope means the line rises as you move to the right, while a negative slope means it falls. The y-intercept, (b), provides a clear starting point for graphing the line, giving the exact point where the line crosses the vertical axis.

In practical applications, using the slope-intercept form simplifies tasks like graphing the line or performing calculations involving that line, making it a foundational concept in algebra.