The rate of change in a linear equation refers to how much the dependent variable changes for a given change in the independent variable. It’s essentially the slope of the line represented by the equation.
In a linear equation written in the format y = mx + b, the letter m represents the slope, which is the rate of change. This means that for every unit increase in x, y changes by m units.
For example, if we have a linear equation y = 2x + 3, the slope is 2. This indicates that for every increase of 1 in x, y increases by 2. If x goes from 1 to 2, y goes from 5 to 7 (2 unit increase).
Thus, the rate of change in a linear equation is constant throughout its domain, which is a defining characteristic of linear relationships.