Creating Equations for Lines of Best Fit

This video tutorial explains the connection between scatterplots, lines of best fit, and equations. It reviews linear equations in the form y = mx + b, where m is the slope and b is the y-intercept. The tutorial demonstrates how to draw a trendline on a scatterplot and write its equation by identifying the y-intercept and slope. Two examples are provided: one showing the relationship between study time and student scores, and another illustrating the connection between temperature and gas bills. The video concludes with a summary of the process for creating lines of best fit and writing their equations.

What is the standard form of a linear equation?

• y = mx + b

• y = bx + m

• y = m/b + x

• y = b/m + x

What does 'm' represent in the linear equation form?

• Y-intercept

• X-intercept

• Slope

• Coefficient of x

What is the first step in creating a line of best fit for a scatterplot?

• Calculate the slope

• Identify two points

• Draw the trendline

• Write the equation

How do you find the slope of a line from a graph?

• Add the y-values of two points

• Divide the change in y by the change in x

• Subtract the y-values of two points

• Multiply the x-values of two points

What points did the teacher use to calculate the slope in the example?

• (15, 70) and (0, 40)

• (25, 80) and (0, 49)

• (20, 75) and (0, 45)

• (30, 85) and (5, 50)

What is the approximate y-intercept in the gas bill example?

• 122

• 123

• 120

• 121

What method did the teacher prefer for finding the slope?

• Algebraically

• Estimation

• Using a calculator

• Graphically

How can you verify the accuracy of a trendline equation?

• Use another point to check the equation

• Change the y-intercept

• Calculate another slope

• Draw another line

What should the y-value be approximately when x is 40 in the gas bill example?

• 83.67

• 85.67

• 86.67

• 84.67

What is the primary goal when drawing a line of best fit through a scatterplot?

• To connect the highest and lowest points

• To pass through every point

• To minimize the distance to all points

• To pass through the center of the data