2.8 Rewrite Equations and FormulasEssential Question: How do you write equations

and formulas?

Warm-up: Define the following:1. Square root 8. Identity2. Radicand 9. ratio3. Perfect square 10. proportion4. Irrational number 11. cross

products5. Real numbers 12. scale

drawing6. Inverse operations 13. scale7. Equivalent equations 14. literal equation

CommonCoreCC.9-12.A.CED.4Rearrange formulas to highlight a quantity of interest, usingthe same reasoning as insolving equations

9-23-14

2.7 Exercises 2-30 Even page 123

• 2) Measure the distance in cm, in the drawing and then substitute the value in the proportion:

4) 7 6) 6 8) 6 10) 7 12) 27 14) 26 16) D 18) Distribute the 14 to both b and 2; 18b = 14b + 28, 4b = 28, b = 720) 2 22) 22 24) -2.5 26) 5.2 28) 7.4

30) -7.1

distance actual

drawingin distance

3

1

Literal Equation

• The equation ax + b = c is called a literal equation because the coefficients and constants have been replaced by letters.

• When you solve a literal equation, you can use the result to solve any equation that has the same form as the literal equation.

Subtract b from each side.

Write original equation.

Solve ax + b = c for x.STEP 1

SOLUTION

Solve ax + b = c for x. Then use the solution to solve 2x + 5 = 11.

Solve a literal equationEXAMPLE 1

xc – b

a=

ax + b = c

ax = c – b

Assume a 0. Divide each side by a.

The solution of 2x + 5 = 11 is 3.ANSWER

Simplify.

Substitute 2 for a, 5 for b, and 11 for c.

Solution of literal equation.

Use the solution to solve 2x + 5 = 11.STEP 2

Solve a literal equation

EXAMPLE 1

11 – 52=

x = c – b

a

= 3

GUIDED PRACTICE for Example 1

1. a – bx = c; 12 – 5x = –3

Solve the literal equation for x. Then use the solution to solve the specific equation

; 3ANSWER x = a – c

b

GUIDED PRACTICE for Example 1

2. ax = bx + c; 11x = 6x + 20

Solve the literal equation for x. Then use the solution to solve the specific equation

; 4ANSWERc

x = a – b

Two or More Variables

• An equation in two variables, such that 3x +2y = 8, or a formula in two or more variables, such as A = ½ bh, can be rewritten so that one variable is a function of the other variable(s).

Divide each side by 2.

Write original equation.

Write 3x + 2y = 8 so that y is a function of x.

EXAMPLE 2 Rewrite an equation

Subtract 3x from each side.

3x + 2y = 8

2y = 8 – 3x

3

2y = 4 – x

Multiply each side by 2.

Write original formula.

SOLUTION

Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters.

b.

Solve the formula for the height h.a.

EXAMPLE 3 Solve and use a geometric formula

The area A of a triangle is given by the formula A = bh where b is the base and h is the height.

12

a. bh1

2A =

2A bh=

Substitute 64.4 for A and 14 for b.

Write rewritten formula.

Substitute 64.4 for A and 14 for b in the rewritten formula.

b.

Divide each side by b.

EXAMPLE 3 Solve and use a geometric formula

2A

bh=

= 2(64.4)

14

= 9.2 Simplify.

ANSWER The height of the triangle is 9.2 meters.

h2A

b=

GUIDED PRACTICE for Examples 2 and 3

3. Write 5x + 4y = 20 so that y is a function of x.

5

4y = 5 – x ANSWER

GUIDED PRACTICE for Examples 2 and 3

The perimeter P of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width.

a. Solve the formula for the width w.

4 .

w = or w = – lP – 2l

2ANSWER

P

2

GUIDED PRACTICE for Examples 2 and 3

Use the rewritten formula to find the width of the rectangle shown.

b .

2.4ANSWER

EXAMPLE 4 Solve a multi-step problem

You are visiting Toronto, Canada, over the weekend. A website gives the forecast shown. Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Use the formula C = (F – 32) where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit.

59

Temperature

Simplify.

Write original formula.

EXAMPLE 4 Solve a multi-step problem

Multiply each side by , the reciprocal of .

955

9

Add 32 to each side.

SOLUTION

STEP 1 Rewrite the formula. In the problem, degrees Celsius are given and degrees Fahrenheit need to be calculated. The calculations will be easier if the formula is written so that F is a function of C.

(F – 32)5

9C =

F – 32C9

5=

9

5C + 32 = F

· (F – 32)9

5

5

9C

9

5=

EXAMPLE 4 Solve a multi-step problem

ANSWER

9

5=The rewritten formula is F C + 32.

The low for Saturday is 57.2°F.

ANSWER

= 25.2 + 32

Saturday (low of 14°C)

Find the low temperatures for Saturday and Sunday in degrees Fahrenheit.

EXAMPLE 4 Solve a multi-step problem

STEP 2

Sunday (low of 10°C)

= (14)+ 329

5 = (10)+ 329

5

= 18 + 32

= 57.2 = 50

C + 329

5 F = F C + 32

9

5=

The low for Sunday is 50°F.

ANSWER

GUIDED PRACTICE for Example 4

Use the information in Example 4 to find the high temperatures for Saturday and Sunday in degrees Fahrenheit.

5.

71.6°F, 60.8°FANSWER

Classwork

•2.8 Exercises •2-26 even

•Pages 129-130