1. Using Substitution to Evaluate Algebraic Expressions and Formulas
Section 1.8
Using Substitution to Evaluate Algebraic Expressions and Formulas

2. Evaluating Algebraic Expressions
The order of operations is used to evaluate variable expressions.
When we replace a variable by a particular value, we say we have substituted the value for the variable.

3. Example
Evaluate 3x – 2 for x = 8. 3x – 2 = 3(8) – 2 = –24 – 2 = –26

4. Example
Evaluate for x = 3. a. b.

5. Example
Evaluate 5x2 – 3x + 4y for x = 2 and y = 6. 5x2 – 3x + 4y = 5(2)2 – 3(2) + 4(6) = 5(4) – 3(2) + 4(6) = 20 – 6 – 24 = –10

6. Geometry Review
A formula can be evaluated by substituting values for the variables.
The perimeter (P) is the distance around a figure.
The area (A) is the measure of the amount of surface in a region. A A

7. Common Geometric Formulas
Parallelogram
A = ab
P = 2b + 2c
Rectangle
A = lw
P = 2l + 2w
Square
A = s2
P = 4s a c b w l s

8. Common Geometric Formulas
Triangle
A = ab
P = sum of all three sides
Trapezoid
A = a(b1 + b2)
P = sum of all four sides
Circle
A = πr2
(π = 3.14)
C = πd a b d a b2 e b1
d =2r r
r is the radius
d is the diameter

9. Example
Find the perimeter of the parallelogram. P = 2l + 2w = 2(11) + 2(7) = = 36
11 m
7 m
The perimeter of the parallelogram is 36 m.

10. Example Find the area of the trapezoid.
8 mm
5.5 mm
6 mm
The area of the trapezoid is 38.5 mm2.

11. Example Find the area of the triangle.
The area of the triangle is in2.

12. Example
Find the circumference and area of a circle whose radius is 15 feet.
The diameter is twice the radius. 15
The circumference is approximately 94.2 ft and the area is approximately ft2.