Study Notes on Wellness and Graphing Linear Equations

Wellness and Line Graphing Concepts

Overview of Line Graphing

• Purpose: To understand how to graph linear equations and determine their forms.

Standard Form of Linear Equations

• Standard Form Definition: A linear equation in two variables is written as $Ax + By = C$ where:
  • $A$, $B$, and $C$ are integers,
  • $A$ and $B$ are not both zero.

Examples of Equations

1. First Equation: $y = 4.3x$

   • Analysis: This is a linear equation because it can be rewritten in standard form.
   • Rewritten Form: $-4.3x + y = 0$ (Here, $A = -4.3$, $B = 1$, and $C = 0$)

2. Second Equation: $by - 3 = 0$

   • Analysis: This is also a linear equation.
   • Rewritten Form: Assuming the equation can be rearranged as $y = \frac{3}{b}$

3. Third Equation: $3x - y = 4$

   • Analysis: This one is in standard form and is clearly a linear equation.

Conclusion on Linearity:

• The concept of linear equations is fundamental in graphing.

• If an equation can be rearranged into the form $Ax + By = C$, it is considered linear.

• A linear equation will produce a straight line when graphed on a coordinate plane.