1. Rewrite Formulas and Equations
Section 1-4
Rewrite Formulas
and Equations

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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

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

11. Example 4 - Continued Find the value of y when x = 3. y = 8 (2x – 5)
(2(3) – 5)
y =
(6 – 5)
y = 8

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