Use the equation of a linear model to solve problems in the context of bivariate measurement data

What you'll learn

1. Write the equation y = mx + b for an informally fitted line on a scatter plot by identifying the slope and y-intercept from the graph or data
2. Interpret the slope of a linear model in context, using the language "for each additional unit increase in [x], [y] is associated with a change of [m] units"
3. Interpret the y-intercept of a linear model in context and evaluate whether the intercept has a meaningful real-world interpretation for the given data
4. Use the equation of a linear model to make predictions by substituting values of the explanatory variable, distinguishing between interpolation (within the data range) and extrapolation (beyond the data range)
5. Recognize the limitations of a linear model, including that predictions from extrapolation may be unreliable and that association does not imply causation

Prerequisites

• Know that straight lines are widely used to model relationships between two quantitative variables
• Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line