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 | |

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

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. ## 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

Calculator Click |
What You See |
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 × 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 = 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 = 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