Linear growth

Definition

Linear growth describes a situation where a quantity increases by a constant amount over equal intervals of time. It is represented mathematically by the equation $y = mx + b$, where $m$ is the rate of growth and $b$ is the starting value.

5 Must Know Facts For Your Next Test

1. The graph of linear growth is a straight line with a constant slope.
2. In linear growth, the first differences (the differences between consecutive values) are constant.
3. Linear growth can be contrasted with exponential growth, which increases by a constant factor rather than a constant amount.
4. The slope ($m$) in the equation $y = mx + b$ represents the rate of change or growth per unit time.
5. Applications of linear growth include situations like saving money at a fixed interest rate or traveling at a constant speed.

Review Questions

• What distinguishes linear growth from exponential growth in terms of their respective equations?
• How do you determine the slope and y-intercept in the equation $y = mx + b$?
• What does it mean when we say that linear growth has 'constant first differences'?

Related terms

Exponential Growth: A type of growth where a quantity increases by a constant percentage over equal intervals of time, typically modeled by the equation $y = ab^x$.

Slope: A measure of the steepness or incline of a line, often denoted as $m$ in the linear equation $y = mx + b$. It represents the rate of change.

Y-intercept: The point where the graph of an equation intersects the y-axis. In the equation $y = mx + b$, it is denoted as $b$.