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Section 1-4
Rewrite Formulas and Equations
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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.
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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
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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
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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
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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
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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
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Example 3Solve 5x + 3y = 8 for y.
5x + 3y = 8 - 5x -5x
3 3 3 3y = - 5x + 8
y = -5x + 8 3 3
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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
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Example 4Solve 2xy – 5y = 8 for y.
2xy – 5y = 8 y(2x – 5) = 8 (2x – 5) (2x – 5)y = 8 (2x – 5)
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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
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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)