Linear functions can be represented by a straight line in space. One way to define a straight line uniquely is to use its slope (or direction vector) and any one point on the line.
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Condition of Parallelism: The Slope of two (lines) linear functions must be equal. i.e. m1=m2 Condition of perpendicularity : The product of slope of two (lines) linear functions must be equal to - 1. i.e. m1.m2=-1
In mathematics, a constant rate of change is called a slope. For linear functions, the slope would describe the curve of the function. The world "constant" in this context means the slope and therefore angle of the curve will not change.
A linear relationship means that the slope of the line is proportional, which means that the line is straight. In contrast to the linear realtionship, the non-linear relationship's slope is not proportional and the line will curved and not straight. Formula of calculating the slope is the difference of y divided by the difference of x.
First of all, many relationships are inherently linear. For example, distance travelled is a linear function of time where the slope is speed. Beyond that, linear functions are extremely simple. Because of this they can be used to model pieces of more complicated functions in a simple way. Thus, you can study the properties of the complicated function by studying a piece of it at a time, in a sense. Many mathematical objects can be said to behave as linear operators. This means that a firm undertstanding of lines, slopes and linear functions transfers to these objects. Linearity is fundamental to a great deal of mathematics.
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