The steepness
or slope of a line is the ratio of the vertical change to the
horizontal change.
The slope
of a line can be determined if two points on that line are provided.
Algebraically, this can be calculated
by the formula:
where m represents the slope, the
numerator shows the y, and the
denominator
indicates the x.
Example
Given
the points (3, 5) and (1, 4) are both contained on the same line,
the
slope of this line is
Four
Basic Types of Slope
Positive 
Negative 
Zero 
Undefined 




Positive Slope: the line rises to the right
Negative Slope: the line falls to the right
Zero Slope: the line is horizontal (every ycoordinate is the same)
Undefined Slope: the line is vertical (every xcoordinate is the same)
Finding
Slope in Excel
Given two xcoordinates and
two ycoordinates, we can also use Excel to find the slope of
a line.
Click here
to learn how to find slope using Excel.
Parallel
and Perpendicular Lines
Parallel Lines
(Slopes are Equal)

Perpendicular Lines
(Slopes are Opposite Reciprocals)



for both lines m = 2 
m = 1 and m = 1 
Finding Slope
Given a Line
Examples
Find 2 clearly defined points. Determine
the necessary rise and run to get from one point to the other.
Graph 1:
Find (0, 3). In order to get from this
point to (1, 1), you must rise 3 times and run 1 time.
Graph 2:
Find (0, 1). Getting from this point to
(3, 1) requires that you rise 2 and run 3.
Click here
to begin student activity
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