Section 1-4
Day 1 - Rewrite
Formulas
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
Distance
Formula
d = rt
Meaning of
Variables
d = distance
r = rate
t = time
F = degrees Fahrenheit
Temperature
Area of a Triangle
Area of a Rectangle
F = 9 C + 32
5
C = degrees Celsius
A = ½bh
A = area
b = base
h = height
A = lw
A = area
l = length
w = width
Quantity
Perimeter of a
rectangle
Area of a Trapezoid
Area of a Circle
Circumference of a
Circle
Formula
Meaning of
Variables
P = 2l + 2w
P = perimeter
l = length
w = width
A = ½(b1 + b2)h
A = area
b1 = one base
b2 = other base
h = height
A = Πr2
A = area
r = radius
C = 2Πr
C = circumference
r = radius
Example 1
Solve the formula d = rt for t.
d = rt
r r
t = d
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
Example 2
Solve the formula A = ½(b1 + b2)h for b2.
2 • A = ½(b1 + b2)h • 2
2A = (b1 + b2)h
h
h
2A = b1 + b2
h
-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.
2A – b1 = b2
h
2(105) – 13 = b2
10
21 – 13 = b2
b2 = 8 cm
Homework
Section 1-4 Day 1
Pages 30 – 32
1-6, 18, 20, 33, 35
Section 1-4
Day 2 - Rewrite Linear
Equations
Example 1
Solve 5x + 3y = 8 for y.
5x + 3y = 8
- 5x
-5x
3y = - 5x + 8
3
3
3
y = -5x + 8
3 3
Example 1 - Continued
Find 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
y = 11
3
Example 2
Solve 15x + 4y = 9 for y.
15x + 4y = 9
- 15x
-15x
4y = - 15x + 9
4
4
4
y = -15x + 9
4
4
Example 2 - Continued
Find the value of y when x = -3.
y = -15x + 9
4
4
y = -15(-3) + 9
4
4
y = 45 + 9
4
4
27
y = 54
y=
2
4
Homework
Section 1-4 Day 2
Pages 30 – 31
7-16
Section 1-4
Day 3 - Rewrite
Nonlinear equations
Example 1
Solve xy – 3x = 40 for y.
xy – 3x = 40
+ 3x +3x
xy = 40 +3x
x
x
y=
40 + 3x
x
Example 1 - Continued
Find the value of y when x = 5.
y = 40 + 3x
x
y = 40 + 3(5)
(5)
y=
y = 11
55
5
Example 2
Solve 2xy – 5y = 8 for y.
2xy – 5y = 8
y(2x – 5) = 8
(2x – 5) (2x – 5)
y=
8
(2x – 5)
Example 2 - Continued
Find the value of y when x = 3.
y=
8
(2x – 5)
y=
8
(2(3) – 5)
y=
8
(6 – 5)
y= 8
Homework
Section 1-4 Day 3
Pages 31 – 32
22-26
40-52 even