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**Rewrite Formulas and Equations**

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 Distance d = rt Temperature A = ½bh A = lw**

Meaning of Variables Distance d = rt d = distance r = rate t = time Temperature F = 9 C + 32 5 F = degrees Fahrenheit C = degrees Celsius Area of a Triangle A = ½bh A = area b = base h = height Area of a Rectangle A = lw l = length w = width

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**Quantity Formula P = 2l + 2w A = Πr2 C = 2Πr Perimeter of a rectangle**

Meaning of Variables Perimeter of a rectangle P = 2l + 2w P = perimeter l = length w = width Area of a Trapezoid A = ½(b1 + b2)h A = area b1 = one base b2 = other base h = height Area of a Circle A = Πr2 r = radius Circumference of a Circle C = 2Πr C = circumference

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**Example 1 Solve the formula d = rt for t. t = d d = rt r r r**

• Find the time it takes to travel 312 miles at an average rate of 48 miles per hour. t = 312 48 t = 6.5 hours

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

2 • A = ½(b1 + b2)h • 2 2A = (b1 + b2)h h h 2A = b1 + b2 h -b 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. 2A – b1 = b2 h 2(105) – 13 = b2 10 21 – 13 = b2 b2 = 8 cm

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

y = -5x + 8

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**Example 3 - Continued Find the value of y when x = -5. y = -5x + 8 3 3**

y = -5(-5) + 8 y = y = 33 3 y = 11

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**Example 4 Solve 2xy – 5y = 8 for y. 2xy – 5y = 8 y(2x – 5) = 8**

(2x – 5) (2x – 5) y = (2x – 5)

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**Example 4 - Continued Find the value of y when x = 3. y = 8 (2x – 5)**

(2(3) – 5) y = (6 – 5) y = 8

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**Homework Section 1-4 Day 1 Pg 30 – 32 (3 – 6, 18 - 20, 32, 34, 35, 36)**

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