Writing Equations for Lines of Best Fit
Writing equations for lines of best fit is a Grade 11 Algebra 1 skill from enVision Chapter 3 that uses the point-slope method on the trend line of a scatter plot. Select two points the line passes through or near, calculate slope m = (y2-y1)/(x2-x1), then write the equation. For study hours vs. test scores, if the trend line passes through (2, 75) and (6, 95): slope = (95-75)/(6-2) = 5 points per study hour, giving y - 75 = 5(x - 2). This equation can predict scores for any number of study hours within the data range.
Key Concepts
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.
Common Questions
How do you write the equation of a line of best fit from a scatter plot?
Identify two points the trend line passes through or near, calculate slope m = (y2-y1)/(x2-x1), then write the equation using point-slope form: y - y1 = m(x - x1).
Study hours vs test scores: trend line through (2,75) and (6,95). Write the equation.
Slope = (95-75)/(6-2) = 5 points/hour. Using point (2,75): y - 75 = 5(x - 2). Simplifies to y = 5x + 65.
Temperature vs ice cream sales: trend line near (70,120) and (90,200). Write the equation.
Slope = (200-120)/(90-70) = 80/20 = 4 sales per degree. Using point (70,120): y - 120 = 4(x - 70).
Why choose points on the trend line, not necessarily data points?
The trend line may not pass through actual data points. Using points on the drawn line gives the equation for that line, not for individual data points.
What does the slope represent in a line of best fit equation?
The rate of change in the trend. A slope of 5 for study hours vs scores means each additional study hour predicts 5 more points.
What is the difference between line of best fit equation and actual data values?
The line of best fit gives predicted values. Actual data points may fall above or below the line. The vertical difference is the residual.