3-7 HW: Pg. 179-181 #6-18eoe, 20-28e, 33-35, 41-42

41. C 42. C

Wir2.5• LESSON

3-8 Rewrite Equations and Formulas

Function Form:

Literal Equation:

an equation that contains 2 or more variables

an equation in x and y written so the dependent variable y is isolated on one side of the equation.

- SOLVE FOR y- function of y in terms of x

Subtract b from each side.

Write original equation.

Solve ax + b = c for x.STEP 1SOLUTION

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 – bAssume 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.STEP 2

11 – 52=

x = c – b

a

= 3

– b - b a a

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

2. ax = bx + c; 11x = 6x + 20 ; 4ANSWERc

x =a – b

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

32

y = 4 – x

– 3x - 3x

2 2

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 formulaThe area A of a triangle is given by the formula A = bh

where b is the base and h is the height.

12

a. bh12A =

2A bh=

Divide each side by b.2A b

h=

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.

= 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.

54

y = 5 – x ANSWER

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

P2

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 .

9

55

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)59C =

F – 32C95

=

95C + 32 =F

· (F – 32)95

59C9

5=

ANSWER 95=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)+ 3295 = (10)+ 32

95

= 18 + 32

= 57.2 = 50

C + 3295

F = F C + 3295=

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

Summary• How do you rewrite equations?• Ans: Use inverse operations to get the needed variable

alone on one side.• Describe and correct the error in the following problem:

• Ans: You need to subtract b to move it to the other side, so ax = -b, so the answer is x = -b/a

Solve the equation for x: 0

ax b

b

b

x

x

a

a

Check Yourself

Pg. 187-189 #4-22e, 28, 32, 38-39

and

Quiz on Pg. 189 #1-8