Section 1-3:
Graphing Data
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.
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.
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.
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.
Linear, Quadratic, Root, and Inverse Relationships
Quadratic
In a Relationship
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 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 Relationships
Root Curve
On a graph, y is proportional to the square root of x.
The equation for a root curve is
yk
x