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
| Input | Display | 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
| Input | Display | 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
| Input | Display | Comment |
|
blinker | clears screen |
6  + 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
| Input | Display | 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. Parentheses protect order of operations. |
|
-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
| Input | Display | Comment |
|
blinker | clears screen |
| 6 + 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 x 4 +25
T = 165
| Input | Display | 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 = 
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 = √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