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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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Is circumference a linear function of diameter?
circumference = pi*d so it is a linear function. If d is multiplied by x, so is the circumference.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
What is a linear function that goes through the origin?
it is just that- a linear function that goes through ther origin. ======================================================= Any equation y = ax, where a is a constant, will do so.
Are all linear equations functions why or why not?
The equation x=c where c is a constant is the equation of a vertical line. It can't be a function but it is linear so the answer is no. For example, the vertical line produced by the linear equation x = 3 does not represent a function. We cannot write this equation so that y is a function of x because the only x-value is 3 and this "maps" to every real-number y.
Is 3x plus 27 equals 8 a quadratic function?
No it is a linear one. X^2 = quadratic, x = linear. So if the equation doesn't have an x squared, then it is not quadratic.
