Writing Equations for Lines of Best Fit

This lesson explains the connection between scatter plots, lines of best fit, and equations. It covers how to write an equation for a line of best fit by identifying the y-intercept and slope. The y-intercept is where the line crosses the y-axis, and the slope is the ratio of change in y to change in x. The lesson provides examples using real data, such as student grades and gas bills, to illustrate how to calculate and interpret these values. It also addresses common misunderstandings about y-intercepts in equations.

What is the main focus of this lesson?

• Exploring the Pythagorean theorem

• Understanding quadratic equations

• Learning about scatter plots, lines of best fit, and equations

• Studying the properties of circles

What does the y-intercept represent in a graph?

• The point where the line crosses the x-axis

• The slope of the line

• The point where the line crosses the y-axis

• The steepness of the line

How is the slope of a line defined?

• The initial value of the line

• The change in x to the change in y

• The point where the line crosses the y-axis

• The change in y to the change in x

What is the equation used to represent a line on a graph?

• y = ax^2 + bx + c

• y = x + b

• y = mx + c

• y = mx + b

In the equation y = mx + b, what does 'm' stand for?

• The initial value

• The x-intercept

• The slope

• The y-intercept

If the y-intercept is 4 and the slope is 3/5, what is the equation of the line?

• y = 4x + 3/5

• y = 3/5x + 4

• y = 4x + 5/3

• y = 5/3x + 4

What is the initial value in the example where the y-intercept is 47?

• 0

• 47

• 15

• 20

How do you simplify the slope if the change in points is 20 and the change in minutes is 15?

• 1.33

• 4/3

• 1.5

• 3/4

What does the equation y = -0.9x + 120 mean in the context of the gas bill example?

• The gas bill increases by 90 cents for every degree increase in temperature

• The gas bill starts at $120 and increases by 90 cents for every degree increase in temperature

• The gas bill starts at $120 and decreases by 90 cents for every degree decrease in temperature

• The gas bill decreases by 90 cents for every degree increase in temperature

What does it mean if the y-intercept is zero in an equation?

• There is no y-intercept

• The initial value is zero

• The line does not cross the y-axis

• The slope is zero