Linear Relationships: A linear relationship represents a straight line . A linear equation describes a line through a set of points, with the depend...
Linear Relationships:
A linear relationship represents a straight line.
A linear equation describes a line through a set of points, with the dependent variable on the independent variable.
The slope of the line indicates the rate of change between the variables.
A linear relationship is typically represented by a linear equation.
Quadratic Relationships:
A quadratic relationship is more complex and describes a parabola.
A quadratic equation is a special case of a linear equation.
The graph of a quadratic relationship is a parabola.
The equation for a quadratic relationship is of the form of y = ax² + bx + c, where a, b, and c are constants.
The value of a indicates the shape of the parabola.
The value of b indicates the turning point of the parabola.
The value of c indicates the vertex of the parabola.
Key Differences:
| Feature | Linear Relationship | Quadratic Relationship |
|---|---|---|
| Shape | Straight line | Parabola |
| Equation | y = ax + b | y = ax² + bx + c |
| Slope | Constant | Variable |
| Turning point | No turning point | At (0, c) |
| Vertex | No vertex | At (a, b) |