# Plug-In

Basics

An algebraic “plug-in” question simply requires you to plug in a number for a letter.

Plugging-In is also known as Substitution.

Linear Expression
Definition
An algebraic statement that performs functions of addition, subtraction, multiplication, and division.  Exponents and roots are not allowed.

Example
x + y + 3

Question
What is the value x + y + 3 when x = 6 and y = 9?

Answer
18

Answer Process
x + y + 3
Plug in 6 for x.
Plug in 9 for y.
6 + 9 + 3
18

Calculator Click What You See Comment
blinker clears screen
6 + 9 + 3 6+9+3 x + y + 3
Plug in 6 for x.
Plug in 9 for y.
18 Answer
###### Plug-In

Linear Equation
Definition
A linear expression with an = sign.

Example
y = x + 3

Question
What is the value of y when y = x + 3 and x = 6?

Answer
9

Answer Process
y = x + 3
Plug in 6 for x.
y = 6 + 3
y = 9

Calculator Click What You See Comment
blinker clears screen
6 + 3 6+3 y = x + 3
Plug in 6 for x.
9 Answer
###### Plug-In

Polynomial Expression

Definition
An algebraic statement that performs functions of addition, subtraction, multiplication, and division.  Exponents and roots are allowed.

Example
x² + y + 3

Question
What is the value of x² + y + 3 when x = 6 and y = 8?

Answer
47

Answer Process
x² + y + 3
Plug in 6 for x.
Plug in 8 for y.
6² + 8 + 3
47

Calculator Click What You See Comment
blinker clears screen
+ 8 + 3 6²+8+3 x² + y + 3
Plug in 6 for x.
Plug in 8 for y.
47 Answer
###### Plug-In

Example
24y – 6x²

Question
What is the value of 24y – 6x² when x = -7 and y = 3?

Answer
-222

Answer Process
24y – 6x²
Plug in -7 for x.
Plug in 3 for y.
24 × 3 – 6 × (-7)²
When squaring a negative number, parentheses protect the order of operations.
-222

Calculator Click What You See Comment
blinker clears screen
24 × 3 – 6 ×
-7
24*3-6*(-7)² 24y – 6x²
Plug in -7 for x.
Plug in 3 for y.

-222 Answer
###### Plug-In

Polynomial Equation

Definition
A polynomial expression with an = sign.

Example
y = x² + 3

Question
What is the value of y when y = x² + 3 and x = 6?

Answer
39

Answer Process
y = x² + 3
Plug in 6 for x.
y = 6² + 3
y = 36 + 3
y = 39

Calculator Click What You See Comment
blinker clears screen
+ 3 6²+3 y = x² + 3
Plug in 6 for x.
39 Answer
###### Plug-In

Algebraic Word Problem
Definition
An algebraic problem requiring translation of Everyday language into Math action.

Example
The total cost T of renting a car is $35.00 times the number of days d the car is rented plus a one-time charge of$25.00.
T = 35d + 25

Question
The total cost T of renting a car is $35.00 times the number of days d the car is rented plus a one-time charge of$25.00.  What is the value of T when T = 35d + 25 and the car is rented for 4 days?

Answer
$165.00 Answer Process T = 35d + 25 Plug in 4 for d. T = 35 × 4 + 25 T = 165 Calculator Click What You See Comment blinker clears screen 35 × 4 + 25 35*4+25 T = 35d + 25 Plug in 4 for d. 165 Answer ###### Plug-In Practice – Questions 1. What is the value of x + y + 3 when x = 7 and y = 11? 2. What is the value of y when y = x + 12 and x = 13? 3. What is the value of x² + y + 9 when x = 4 and y = 5? 4. What is the value of y when y = x² + 8 and x = 3? 5. What is the value of 4x – 14y² when x = -5 and y = -3? 6. The total cost T of renting an apartment is$1200 a month times the number of months m the apartment is rented plus a one-time deposit of $600. What is the value of T where T = 1200m + 600 and the apartment is rented for 12 months? 7. An apartment rents for$1200 times the number of months m it is occupied plus a one-time deposit of $600. Three roommates are sharing the cost of the apartment. What is the cost C for each roommate where C = $\bf\displaystyle\frac{1200m + 600}{3}$ and the apartment is rented for 12 months? 8. It costs$10.00 to set up a lemonade stand.  The stand will charge 25 cents for each cup c of lemonade that it sells.
What is the amount of money M the stand makes where M = 0.25c – 10 for 61 cups of lemonade sold?

9.  The area of a room is represented by the formula A = l × w, where A = area, l = length, and w = width.
What is the area (in square feet) of a room where l = 8.5 feet and w = $\bf\displaystyle\sqrt{82}$ feet?

10.  The slope-intercept form of the equation of a line is y = mx + b.
What is the value of y when m = 4, x = 7, and b = 5?

Practice – Answers
1.  21

2.  25

3.  30

4.  17

5.  106

6.  $15000 7.$5000

8.  \$5.25

9.  76.97077367 square feet

10.  33