Section 1-4

Rewrite Formulas and Equations

Vocabulary• Formula – An equation that relates

two or more quantities.

• Solve for a Variable – Rewrite an equation as an equivalent equation in which the variable is on one side and does not appear on the other side.

Quantity Formula Meaning of Variables

Distance d = rtd = distancer = ratet = time

Temperature

F = 9 C + 32 5

F = degrees Fahrenheit

C = degrees Celsius

Area of a Triangle

A = ½bhA = areab = baseh = height

Area of a Rectangle

A = lwA = areal = lengthw = width

Quantity Formula Meaning of Variables

Perimeter of a rectangle

P = 2l + 2wP = perimeterl = lengthw = width

Area of a Trapezoid

A = ½(b1 + b2)h

A = areab1 = one baseb2 = other baseh = height

Area of a Circle A = Πr2A = arear = radius

Circumference of a Circle

C = 2ΠrC = circumferencer = radius

Example 1Solve the formula d = rt for t.

d = rt t = d r r r

• Find the time it takes to travel 312 miles at an average rate of 48 miles per hour.

t = 6.5 hours

t = 312 48

Example 2Solve the formula A = ½(b1 + b2)h for b2.A = ½(b1 + b2)h

2A = (b1 + b2)h

2 •

2A = b1 + b2

h

h h

• 2

-b1 -b1

2A – b1 = b2

h

Example 2 - Continued• Find the length of the other base of a trapezoid if the length of one base is 13 cm, the height is 10 cm, and the area is 105 cm2.

21 – 13 = b2

2(105) – 13 = b2

10

b2 = 8 cm

2A – b1 = b2

h

Example 3Solve 5x + 3y = 8 for y.

5x + 3y = 8 - 5x -5x

3 3 3 3y = - 5x + 8

y = -5x + 8 3 3

Example 3 - ContinuedFind the value of y when x = -5.

y = -5x + 8 3 3

y = -5(-5) + 8 3 3 y = 25 + 8 3 3 y = 33 3

y = 11

Example 4Solve 2xy – 5y = 8 for y.

2xy – 5y = 8 y(2x – 5) = 8 (2x – 5) (2x – 5)y = 8 (2x – 5)

Example 4 - ContinuedFind the value of y when x = 3.

y = 8 (2x – 5)

y = 8 (2(3) – 5)

y = 8 (6 – 5)

y = 8

HomeworkSection 1-4

Day 1 Pg 30 – 32 (3 – 6, 18 - 20, 32, 34, 35, 36)

Day 2 Pg 30 – 32 (8,10,12,14, 16, 22, 24,

28-31)