Linear Interpolation and Extrapolation
This Grade 8 math skill from Pengi Math (Grade 8) teaches students to use a trend line to make predictions through linear interpolation (predicting within the data range) and extrapolation (predicting beyond the data range). Students understand the difference between the two and when extrapolation becomes unreliable.
Key Concepts
Property We can model a linear pattern in data using a line of best fit (also called a regression line).
We can use interpolation to estimate values between known data points or extrapolation to predict values beyond the data range.
Predictions made through extrapolation become less reliable the further we move from the original data.
Common Questions
What is linear interpolation?
Linear interpolation is using a trend line to estimate a value within the range of the existing data. It is generally more reliable than extrapolation.
What is linear extrapolation?
Linear extrapolation is using a trend line to predict a value beyond the range of the existing data. It assumes the trend continues, which may not always be true.
How do you use a trend line to make a prediction?
Write the equation of the trend line, then substitute the given x-value to find the predicted y-value.
When does extrapolation become unreliable?
Extrapolation becomes less reliable as you move further from the data range, since the trend may not continue in the same direction.
Where is interpolation and extrapolation taught in Grade 8?
Linear interpolation and extrapolation are covered in the Grade 8 Pengi Math textbook under scatter plots and trend lines.