Recognizing linear functions | Linear equations and functions | 8th grade | Khan Academy

TL;DR

Linear functions have a constant change in y for every change in x, while non-linear functions do not.

Transcript

Deirdre is working with a function that contains the following points. These are the x values, these are y values. They ask us, is this function linear or non-linear? So linear functions, the way to tell them is for any given change in x, is the change in y always going to be the same value. For example, for any one-step change in x, is the change ... Read More

Key Insights

• 💱 Linear functions have a constant rate of change in y for every change in x.
• 💱 Non-linear functions have varying rates of change in y for different changes in x.
• 💱 Dividing the change in y by the change in x helps identify linear or non-linear functions.
• 📈 Graphing the function can provide a visual representation of its linearity.
• 💱 The given function is non-linear because the change in y increases with each change in x.
• 🫥 Linear functions have points that form a straight line on a graph.
• 🫥 Non-linear functions may have points that do not form a straight line on a graph.

Questions & Answers

Q: How can you determine if a function is linear or non-linear?

By checking if the change in y for each change in x is always the same. If it is constant, the function is linear. If it varies, the function is non-linear.

Q: What is the significance of the change in y divided by the change in x?

Dividing the change in y by the change in x helps determine if the function has a constant rate of change. If the quotient is always the same, the function is linear.

Q: Can you give an example of a linear function?

Yes, a linear function could be y = 2x + 3, where for every increase of 1 in x, y increases by 2.

Q: How does graphing the function help determine linearity?

Plotting the points on a graph helps visualize the relationship between x and y. If the points form a straight line, the function is linear. If they do not, the function is non-linear.

Summary & Key Takeaways

• Linear functions have a consistent change in y for every change in x, while non-linear functions do not.

• To determine if a function is linear, divide the change in y by the change in x and check if it is a constant value.

• In the given example, the function is non-linear because the change in y increases with each change in x.