1. Computational Thinking: Pattern Recognition
To find the pattern of linear equation we need to look for the common difference. If a pattern grows or decays by the same amount each time, it is linear.
Example:
In the sequence \(3, 7, 11, 15...\)
The pattern here is "add 4 to the previous number."
2. Constructing Linear Expressions
Once a pattern is identified, we need to change it into the algebraic version. A linear expression is the structure of a starting value plus a repeating change.
Variable \((n)\): The position in the sequence (Term 1, Term 2, etc.).
Coefficient: The "jump" or difference between terms.
Constant: The adjustment needed to reach the first term.
3. Systematic Representation
Systematic representation involves organizing data so the relationship between input \(x\) and output \(y\).
Using the below formula we represent linear equation:
\(y = mx + b\)
Where, \(m\) is the slope and \(b\) is the y - intercept
4. Analyzing Linear Relationships: Equations & Graphs
A linear relationship creates a straight line when plotted.
The Linear Equation: \(y = mx + b\)
The Graph
Visualizing the relationship allows us to get the data.
Positive Slope: The line goes up (growth).
Negative Slope: The line goes down (decay).
Intersection: Where two different linear relationships meet, signifying a point of equality.