3: Linear Functions
- Page ID
- 83698
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- 3.1: Introduction to Linear Functions
- Imagine placing a plant in the ground one day and finding that it has doubled its height just a few days later. Although it may seem incredible, this can happen with certain types of bamboo species. These members of the grass family are the fastest-growing plants in the world. One species of bamboo has been observed to grow nearly 1.5 inches every hour. A constant rate of change, such as the growth cycle of this bamboo plant, is a linear function.
- 3.2: Linear Equations in One Variable
- A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form ax+b=0ax+b=0 and are solved using basic algebraic operations.
- 3.3: Modeling with Linear Functions
- We can use the same problem strategies that we would use for any type of function. When modeling and solving a problem, identify the variables and look for key values, including the slope and y-intercept. Draw a diagram, where appropriate. Check for reasonableness of the answer. Linear models may be built by identifying or calculating the slope and using the y-intercept. The x-intercept may be found by setting y=0, which is setting the expression mx+b equal to 0.