The slope (rate of change) of a segment or a line, generally denoted by the variable corresponds to the value of its incline with respect to the -axis.
The slope of a line corresponds to the ratio of the difference of the -coordinates and the difference of the -coordinates of two points on the line.
When the two points and are given, the slope can be calculated using the following formula.
Calculate the slope of the following segment.
The rate of change (slope) is therefore 2/5. This means that every time 5 units are moved on the positive -axis, 2 units are moved up on the -axis.
Four different inclines can be found depending on the type of slope that is observed.
An increasing line has a positive slope.
A decreasing line has a negative slope.
A horizontal line has a slope of zero.
A vertical line has an undefined slope.
Increasing Line = Positive Slope
Decreasing Line = Negative Slope
Horizontal Line = Zero Slope
Vertical Line = Undefined Slope
With a horizontal segment, the slope is because the numerator is equal to zero ( ).
With a vertical segment, the slope is undefined, because the denominator in the slope calculation is zero ( ). The result of a division by is undefined.
It is possible to determine the slope of a line from the parameters of the equation when the latter is given.
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General form
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Functional form
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Symmetric form
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Slope |
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In a relation between two variables represented by a linear function, the slope is defined as the rate of change.