What you should learn

To graph linear equations

NCTM Curriculm Standards 2, 3, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Linear Equation

 

Introduction: The manner in which you burn Calories depends on your weight and the activity you are doing. The cart below shows the number of Calories burned per minute per kilogram (C/min/kg).

Manual weighs 70 kilograms and wants to know how many Calories he burns playing football. The formula C = wtr, where w is his weight in kilograms, t is the time in minutes, and r is C/min/kg,c an be used to determine how many Calories he burns.

The number of Calories burned is dependent upon how long he exercises. So, t is the independent variable and C is the dependent variable.

When you graph the ordered pairs, a pattern begins to form. The points seem to lie in a line.

Suppose the domain of C = 9.24t is the set of positive real numbers. There would be an infinite number of ordered pairs that are solutions for the equation. If you graphed all the solutions, they would form a line. The line shown in the graph represents all the solutions for C = 9.24t

Since the graph of C = 9.24t is a line, C = 9.24t is called a linear equation.

Linear equations may c ontain one or two variables with no variable having an exponent other than 1.

A linear equation is an equation that can be written in teh form Ax + By = C, where A, B, and C are any real numbers, and A and B are not both zero.

Exercise 1: Determine whiether each equation is a linear equation. If so, ideantify A, B, and C.

a. 4x = 7 + 2y

First rewrite the equation so that both variables are on the same side of the equation.

4x = 7 + 2y

4x - 2y = 7

The equation is now in the form Ax + By = C, where A=4, B=-2, and C=7.

b. 2x - y = 7

c. x = 12

To graph a linear equation, it is often helpful to make a table of ordered pairs that satisfy the equation. Then graph the ordered pairs and connect the points with a line.

Exercise 2: Graph each equation.

a. y = 8x - 4

Select five values for the domain and make a table.

 

Then graph the ordered pairs and connect them to draw the line.

The range of this relation is the set of real numbers.

b. 2x + 5y = 10

Activity: Refer to the introduction. Carmen Delgado is running in a cross-country meet at the rate of 5 min/km. Her weight is 50 kg. How does the number of Calories she is burning compare to those that she would be buring if she were at home word processing her research paper or if she were playing golf with her dad?

Further Application: Assess Yourself. During the next 48 hours, record three activities that you perform and the length of each activity. Determine how many Calories you burned in each activity. In which activity did you burn the most Calories? Explain why you think this activity burned the most Calories.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: to work on the further application problem and these problems in the book: 17 - 59 odd, 61 - 70

Alternative Homework: Enriched: 16 - 56 even, 57 - 70

Extra Practice: Students book page 768 Lesson 5-4

Extra Practice Worksheet: Click Here.

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