Fixed
Fixed
Constant. Not changing or moving.
Example
Problem: Identify which quantities are fixed and which are variable in the equation y = 3x + 7.
Step 1: Look at the numbers in the equation. The coefficients and constants—3 and 7—do not change no matter what value x takes.
y=3x+7
Step 2: The symbols x and y can take on many different values. They are variables.
Step 3: The numbers 3 and 7 are fixed. They remain the same for every (x, y) pair that satisfies the equation.
Answer: In y = 3x + 7, the values 3 and 7 are fixed, while x and y are variable.
Why It Matters
Distinguishing fixed quantities from variable ones is essential for setting up and solving equations correctly. When you know a value is fixed, you treat it as a known constant rather than something to solve for. This distinction appears everywhere—from the fixed rate in a simple interest formula to the fixed acceleration due to gravity in physics equations.
Common Mistakes
Mistake: Confusing fixed values with values that are simply unknown. A letter like 'a' in an equation might represent a fixed constant, not a variable.
Correction: Read the context carefully. In y = ax + b, the letters a and b are typically fixed parameters (set once for a given line), while x and y are the variables that change.
Related Terms
- Constant — A value that is fixed and does not change
- Variable — The opposite—a quantity that can change
- Coefficient — A fixed number multiplied by a variable
- Parameter — A fixed value that defines a specific case