Final answer:
The slope of a linear equation in the form y=mx+b is represented by 'm', demonstrating the line's steepness. The y-intercept is represented by 'b', indicating where the line crosses the y-axis.
Step-by-step explanation:
To determine the rate of change (slope) when given a linear equation in slope intercept form, which is y=mx+b, you would look at the coefficient of x, represented as m in the equation. This coefficient is the slope and it defines the steepness of the line. For example, if the equation is y=3x+9, the slope is 3. This means that for every unit increase in the horizontal axis (x), there is a rise of 3 units in the vertical axis (y). The constant term, b, represents the y-intercept, which is the point where the line crosses the y-axis. In the given example, the y-intercept is 9, indicating that the line crosses the y-axis at y=9.
In the equation y = mx + b, the m represents the slope and the b represents the y-intercept. To determine the slope of a linear equation in slope-intercept form, you need to identify the coefficient of x. This coefficient represents the change in the y-values for each unit change in x-values. For example, if the equation is y = 3x + 2, the slope is 3, which means that for every 1 unit increase in x, the y-value increases by 3 units.