Download 3.8 Lesson

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:
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
Literal Equation:
an equation that contains 2 or more variables
EXAMPLE 1
Solve a literal equation
Solve ax + b = c for x. Then use the solution to solve 2x + 5=11.
STEP 1 Solve ax + b = c for x.
Write original equation.
ax + b = c
–b
- b Subtract b from each side.
ax = c – b
Assume a  0. Divide each side by a.
a
a
c–b
x=
a
c–b
Solution of literal equation.
x = a
11 – 5
Substitute 2 for a, 5 for b, and 11 for c.
= 2
Simplify.
=3
SOLUTION
STEP 2
ANSWER
The solution of 2x + 5 = 11 is 3.
GUIDED PRACTICE
for Example 1
Solve the literal equation for x. Then use the
solution to solve the specific equation
1. a – bx = c; 12 – 5x = –3
2. ax = bx + c; 11x = 6x + 20
ANSWER
a–c
x = b ;3
ANSWER
c
x=
;4
a–b
EXAMPLE 2
Rewrite an equation
Write 3x + 2y = 8 so that y is a function of x.
3x + 2y = 8
– 3x
- 3x
2y = 8 – 3x
2
2
y = 4 – 3x
2
Write original equation.
Subtract 3x from each side.
Divide each side by 2.
EXAMPLE 3
Solve and use a geometric formula
1
The area A of a triangle is given by the formula A = bh
2
where b is the base and h is the height.
a.
Solve the formula for the height h.
Use the rewritten formula to find the
height of the triangle shown, which
has an area of 64.4 square meters.
1
SOLUTION
Write original formula.
a.
A = 2 bh
2A = bh
Multiply each side by 2.
2A
=h
Divide each side by b.
b
b. Substitute 64.4 for A and 14 for b in the rewritten formula.
2A
h= b
Write rewritten formula.
2(64.4) = 9.2 Substitute 64.4 for A and 14 for b. Simplify.
=
14
The height of the triangle is 9.2 meters.
ANSWER
b.
GUIDED PRACTICE
for Examples 2 and 3
Write 5x + 4y = 20 so that y is a function of x.
5
ANSWER y = 5 – x
4
4 . The perimeter P of a rectangle is given by the
formula P = 2l + 2w where l is the length and w is the
width.
3.
a. Solve the formula for the width w.
P – 2l
P
w=
or w =
–l
ANSWER
2
2
b . Use the rewritten formula to find
the width of the rectangle shown.
ANSWER
2.4
EXAMPLE 4
Solve a multi-step problem
Temperature
You are visiting Toronto, Canada, over the weekend.
A website gives the forecast shown. Find the low
temperatures for Saturday and Sunday in degrees
5
Fahrenheit. Use the formula C = (F – 32) where C is
9
the temperature in degrees Celsius and F is the
temperature in degrees Fahrenheit.
EXAMPLE 4
Solve a multi-step problem
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.
5
C = 9 (F – 32)
Write original formula.
9
9 5
9
C = · (F – 32) Multiply each 5side by 5, the
5 9
reciprocal of .
5
9
9
C = F – 32
Simplify.
5
9
C + 32 = F
Add 32 to each side.
5
ANSWER The rewritten formula is F = 9 C + 32.
5
EXAMPLE 4
STEP 2
Solve a multi-step problem
Find the low temperatures for Saturday
and Sunday in degrees Fahrenheit.
Saturday (low of 14°C)
9
F = C + 32
5
9
= 5 (14)+ 32
Sunday (low of 10°C)
9
F = C + 32
5
9
= 5 (10)+ 32
= 25.2 + 32
= 18 + 32
= 57.2
= 50
ANSWER
ANSWER
The low for Saturday
is 57.2°F.
The low for Sunday is 50°F.
GUIDED PRACTICE
for Example 4
5. Use the information in Example 4 to find the
high temperatures for Saturday and Sunday
in degrees Fahrenheit.
ANSWER
71.6°F, 60.8°F
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:
Solve the equation for x: ax  b  0
ax  b
b
x
a
• Ans: You need to subtract b to move it to the other side, so
ax = -b, so the answer is x = -b/a
Check Yourself
Pg. 187-189 #4-22e, 28, 32, 38-39
and
Quiz on Pg. 189 #1-8