Section 1.7

Using Variables and Formulas

1.7 Lecture Guide: Using Variables and Formulas

Objective 1: Evaluate an algebraic expression for specific values of the variables.

Evaluate for each value of x. (Hint: See Technology Perspective 1.7.1 for using a calculator or a spreadsheet to check your work.)

2 4 5x x

1. 2. 3.3x 5x 2x

Evaluate the following expressions for and .

4. 5. 6.

4x 9y

y x 1y x 5 3 10x y

Evaluate the following expressions for and .

7. 8.

3x 5y

44

x yx y

2 2

2 2

46

x yx xy y

Algebraic formulas are used in nearly all areas of mathematics, business, and the sciences. A formula describes a relationship between specific variables. For example, the

area A of a triangle is given by the formula , where b

represents the length of the base of the triangle and h represents the height of the triangle. This relationship holds true for all triangles.

12

A b h

Objective 2: Use algebraic formulas.

Find the area of each triangle. Remember, this area is given in square units.

A = ______9. 4 cm

7 cm

A = ______10.

3 in

8 in

Find the area of each triangle. Remember, this area is given in square units.

The formula for Fahrenheit temperature is given by 11. 9

325

F C . Find the Fahrenheit temperature if the

Celsius temperature C is . 55

12. The formula for the amount in a bank account paying a simple interest rate R for T years is given by ,A P PRT

where P is the principal or initial amount. Find the amount in a bank account after 1 year if there was an initial deposit of $5,000 and the account earned 5% simple interest.

13. The formula for the perimeter of a rectangle is given by 2 2P l w . Find the perimeter P of a rectangle if the

length l is 20 meters and the width w is 35 meters.

One common usage of subscript notation is the slope

formula, , which will be developed in

Chapter 3. This formula is used to calculate m, the slope of a line that passes through the points and .

2 1

2 1

y ym

x x

1 1,x y 2 2,x y

Objective 3: Use subscript notation.

1 1, 3,5x y 2 2, 7,8x y and .

14.Use this formula to calculate the value of m for the line through the points

1 1, 1,4x y 2 2, 2, 3x y and .

15.Use this formula to calculate the value of m for the line through the points

A sequence is an ordered set of numbers with a first number, a second number, a third number, etc. Subscript notation often is used to denote the terms of a sequence: These terms are read a sub one, a sub two, and a sub n, respectively. If a sequence follows a predictable pattern, then we may be able to describe this pattern with a formula for . Consider the sequence 5, 4, 3, 2. Here

1 2, and .na a a

1 25, 4,a a 3 43, and 2.a a na

Use each formula to calculate the first three terms of each sequence.

1 2 3( , ,and )a a a

16. 2 5na n

Use each formula to calculate the first three terms of each sequence.

1 2 3( , ,and )a a a

17. 5 8na n

Objective 4: Check a possible solution of an equation.

A solution of an equation is a value for the variable that satisfies the equation. This means that when the value is substituted for the variable, the expressions on each side of the equation will have the ____________ value.

Check whether each indicated value of x is a solution of the given equation.

18.

(a) Check

(b) Check

1 2 4x x 3x

5x

Check whether each indicated value of x is a solution of the given equation.

19.

(a) Check

(b) Check

2 3 10 0x x 3x

5x

20.

(a) Check

(b) Check

Check whether each indicated value of x is a solution of the given equation.

3 2 24 3

xx

4x

2x

21.

(a) Check

(b) Check

Check whether each indicated value of x is a solution of the given equation.

4 3 2 0x x

43

x

34

x