Independent and dependent variables Chapter Notes | Preparation for EmSAT Grade 8 PDF Download

Introduction

In math, equations can show how things in the real world are related. When an equation has two variables, one is the independent variable, which you choose or control, and the other is the dependent variable, which changes based on the independent one. Think of the independent variable as the input that affects the output, or dependent variable. This guide uses simple examples to explain how these variables work in real-life situations.

Independent and dependent variables 

• Equations often model real-world situations. When an equation with two variables models a real-world situation, one variable is independent and the other is dependent.
• For Examples
  • Example 1: Each sandwich at Sam's Subs costs $5. The equation c = 5s tells you the total cost, c, for s sandwiches.
    The total cost depends on the number of sandwiches. So, c is the dependent variable, and s is the independent variable.
  • Example 2: Marie can read 30 pages in one hour. The equation p = 30h tells you the total number of pages, p, Marie can read if she reads for h hours.
    The number of pages Marie reads depends on the number of hours she spends reading. So, p is the dependent variable, and h is the independent variable.

Tip: You can often think of the independent variable as the input. The dependent variable is the output. You input the independent variable to determine the output, or dependent variable.

Expressions and equations

• An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. Here are some examples of expressions.
  14 ÷ 7
  2x
  5(12 + 2)
  g + 25 – 7
• An equation is a mathematical sentence that says two expressions are equal. Equations always have an equal sign. Here are some examples of equations.
  14 ÷ 7 = 2
  2x = 12
  5(12 + 2) = 90 – 20
  g + 25 – 7 = 7g

Parts of expressions and equations

• Expressions and equations are made up of different parts.
• A variable is a letter that represents an unknown amount. For example, in the equation 2b + 7 = 15, b is the variable.
• A coefficient is a number multiplied by a variable. A coefficient is written immediately in front of the variable. For example, in the expression 9n – 1/2, 9 is a coefficient.
• A constant is a term that contains only a number and no variables. For example, in the equation 7 – 0.6t, 7 is the constant.
• A term is a part of an expression or equation that is added or subtracted. For example, in the expression 3x – 9 + 2/y, 3x, 9, and 2/y are all terms.
• Look at the example below to see how these parts come together to form an expression:
  

Real-world expressions and equations

• You can use expressions and equations to model real-world problems. 
• For Example: Shannon drives 8 miles each time she visits her grandmother. Shannon visits her grandmother v times. You can write an expression for the number of miles Shannon drives to visit her grandmother v times.
  8v