1. Section 1-3: Graphing Data

2. Variables
- Independent Variable (manipulated variable): factor that is changed or manipulated (on x-axis)
- Dependent Variable: the factor that depends on (or responds to) the change in the independent variable (on y-axis)
* The independent variable is the one the experimenter can control directly. The value of the dependent variable depends on the independent variable.

3. Line of Best Fit
When constructing a graph, you must draw a line that best represents ALL of your data.
The Line of best fit is a line that best passes through or near graphed data.
It is used to describe data and predict where new data will appear on the graph.

4. Linear, Quadratic, Root, and Inverse Relationships
Linear Relationship
A linear relationship is a relationship between the x & y variable where the x & y variable are directly proportional (direct variation). As x increases, y increases proportionally.
The graph of a linear relationship is a straight line and is represented by the equation y = mx +b.

5. Linear, Quadratic, Root, and Inverse Relationships
Slope
Slope is calculated using the formula to the right.
ALWAYS select 2 points on the line AS FAR APART AS POSSIBLE.
The y-intercept (b) is the point where the line crosses the y-axis when x is zero.

6. Linear, Quadratic, Root, and Inverse Relationships
Quadratic Relationship
Inverse Relationship
In a quadratic relationship, y varies directly with the square of x.
The equation for a quadratic relationship is y = kx2
The shape of a quadratic relationship is a parabola. Also called a power curve.
In an inverse relationship, y varies inversely of x. As x increases, y decreases.
The equation for a quadratic relationship is y = kx-1 or y = k/x.
The shape of an inverse relationship is a hyperbola.

7. Linear, Quadratic, Root, and Inverse Relationships
Root Curve
On a graph, y is proportional to the square root of x.
The equation for a root curve is