section 1-3: graphing data. variablesvariables - independent variable (manipulated variable): factor...
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Section 1-3:Section 1-3:Graphing DataGraphing DataSection 1-3:Section 1-3:Graphing DataGraphing Data
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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.
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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.
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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.
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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.
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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.
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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