Section 1-3:Section 1-3:Graphing DataGraphing DataSection 1-3:Section 1-3:Graphing DataGraphing Data

VariablesVariablesVariablesVariables

- 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.

Line of Best FitLine of Best FitLine of Best FitLine 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.

Linear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationshipsLinear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationshipsLinear RelationshipLinear 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.

Linear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationshipsLinear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationships

SlopeSlope

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.

Linear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationshipsLinear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationships

Quadratic RelationshipQuadratic 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.

Inverse RelationshipInverse Relationship

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.

Linear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationshipsLinear, Quadratic, Root, and Inverse Linear, Quadratic, Root, and Inverse RelationshipsRelationships

Root Curve Root Curve

On a graph, y is proportional to the square root of x.

The equation for a root curve is y k x