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How can you determine what your income will be in 5 years if you get a 3 percent raise each year?
How do companies predict the amount of money they will earn or spend in a year?
How does a botanist figure out how tall a tree will be in 20 years?
They can use linear equations!
In fact, you can use a linear function to model any real-world situation involving a constant rate of change and an initial value.
A linear equation can be written in slope-intercept form, y is equal to mx plus b.
In this form m is the rate of change and b is the function's initial value.
In this lesson, you will learn when to use a linear function to model a scenario.
You will also learn how to write the function using a table, a graph, or a description of it.
Question
What is the initial value for a function?
A function's initial value is the same as the \( y \)-intercept. It is the value of the output (\( y \)) when the input (\( x \)) is 0.
