Linear growth

Definition

Linear growth is a pattern of increase at a constant rate over equal intervals of time. It can be represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

5 Must Know Facts For Your Next Test

1. Linear growth results in a straight line when graphed on a coordinate plane.
2. The rate of change (slope) in linear growth remains constant.
3. In the equation $y = mx + b$, $m$ represents the constant rate of growth, and $b$ represents the starting value.
4. Linear growth differs from exponential growth, which increases at an increasing rate.
5. Real-world examples of linear growth include arithmetic sequences and uniform motion.

Review Questions

• What is the general form of the equation that represents linear growth?
• How does linear growth differ from exponential growth?
• If given two points on a line that demonstrates linear growth, how would you calculate the slope?

Related terms

Exponential Growth: A pattern of increase where each value is multiplied by a consistent factor over equal intervals of time, often represented as $y = ab^x$.

Slope: The measure of steepness or incline of a line, calculated as the ratio of vertical change to horizontal change between two points $(\Delta y / \Delta x)$.

Y-Intercept: The point where a line crosses the y-axis on a graph, represented by $b$ in the equation $y = mx + b$.