Modeling with Linear Functions

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Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

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Presentation transcript:

Modeling with Linear Functions Section 1.3

What You Will Learn Write equations of linear functions using points and slopes. Find lines of fit and lines of best fi t.

(Take Note)

Ex 1: Writing a Linear Equation from a Graph The graph shows the distance Asteroid 2012 DA14 travels in x seconds. Write an equation of the line and interpret the slope. The asteroid came within 17,200 miles of Earth in February, 2013. About how long does it take the asteroid to travel that distance?

You try The graph shows the remaining balance y on a car loan after making x monthly payments. Write an equation of the line and interpret the slope and y-intercept. What is the remaining balance after 36 payments?

Modeling with Mathematics Two prom venues charge a rental fee plus a fee per student. The table shows the total costs for different numbers of students at Lakeside Inn. The total cost y (in dollars) for x students at Sunview Resort is represented by the equation y = 10x + 600. Which venue charges less per student? How many students must attend for the total costs to be the same?

WHAT IF? Maple Ridge charges a rental fee plus a $10 fee per student. The total cost is $1900 for 140 students. Describe the number of students that must attend for the total cost at Maple Ridge to be less than the total costs at the other two venues. Use a graph to justify your answer.

Finding Lines of Fit and Lines of Best Fit Data do not always show an exact linear relationship. When the data in a scatter plot show an approximately linear relationship, you can model the data with a line of fi t.

Take Note

Line of Best Fit Finding a Line of Fit The table shows the femur lengths (in centimeters) and heights (in centimeters) of several people. Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate the height of a person whose femur is 35 centimeters long.

Cont..

The correlation coefficient (Take Note) The correlation coefficient, denoted by r, is a number from −1 to 1 that measures how well a line fits a set of data pairs (x, y). When r is near 1, the points lie close to a line with a positive slope. When r is near −1, the points lie close to a line with a negative slope. When r is near 0, the points do not lie close to any line.

In Exercises 19–24, use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Find and interpret the correlation coefficient.

Suggested Homework 4, 6, 8, 9,30, 31