Linear Equations and Rate of Change Interpret equations in intercept form using input and output variables Explore the relationships among tables, scatter.

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Presentation transcript:

Linear Equations and Rate of Change Interpret equations in intercept form using input and output variables Explore the relationships among tables, scatter plots, recursive routines, and equations

Equations we have studies Y= x Y=321-13x Y=-30+15x Y= x Y= x Calories burned in a workout Floor heights in a building Earnings from mowing lawns Income from restaurant tabs Distance a car is from Flint Defining variables is important in giving an equation real meaning. In most linear equations, there are different outputs values for different input values. (coefficient of x is different from zero.)

A weather report often describes the actual temperature and indicates temperature you feel as a result of the wind chill factor. This table relates the approximate wind chills for different actual temperatures when the wind speed is 10 mi/h. Assume the wind chill is a linear relationship for temperatures between -5 o and 35 o. Temp ( o F) Wind Chill ( o F)

What are the input and output variables? What is the change in temperature from one table entry to the next? What is the corresponding change in the wind chill? Use the calculator lists to write a recursive routine that generates the table values. What are the missing entries? Temp ( o F) Wind Chill ( o F)

The rate at which the wind chill drops can be calculated from the ratio Explain this ratio. Temp ( o F) Wind Chill ( o F)

The rate of change is equal to the ratio of the change in the output values divided by the corresponding change in the input values. Temp ( o F) Wind Chill ( o F)

Wind Chill Page 188

In this investigation you will use the relationship between temperature and wind chill to explore the concept of rate of change and its connection to tables, scatter plots, recursive routines, equations and graphs. The data in the table represents the approximate wind chill temperatures in degrees F for a wind speed of 20 mi/h. Temperature ( o F) Wind Chill ( o F)

Complete steps 1-4 with your group. Be prepared to share your solutions with the rest of the class. Use the Input/Output Template in your Communicator®. Complete steps 5-8 with your group. Be prepared to share your solutions with the rest of the class. Temperature ( o F) Wind Chill ( o F)