Lesson 3: Use Linear Models to Make Predictions

Property

The slope-intercept form for a linear equation is $y = mx + b$, where $m$ is the slope of the line and the point $(0, b)$ is the y-intercept.

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

This formula calculates the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run).

Property

A line of best fit through a scatter plot can be modeled with a linear equation by selecting two points that the line passes through or nearly passes through.
Use these points $(x_1, y_1)$ and $(x_2, y_2)$ to calculate the slope $m = \frac{y_2 - y_1}{x_2 - x_1}$, then substitute the slope and either point into the point-slope form to write the equation of the line of best fit.

Examples

Property

We can use a line of fit (trend line) drawn through a scatter plot to make predictions about data values.

We can estimate values between known data points or predict values beyond the range of our data using the trend line equation.