Question

I have to write a paragraph explaining what a linear relationship is. Could someone set me in the right direction?

Answer 1

ask...google...bing.....any site should help you with tht look up the definition

Answer 2

ive read what it says on google but it doesn't make sense can you tell me the main part about a linear equation

Answer 3

linearity has two requirements:
1. f(c*x) = c*f(x) : scaling the output by some constant is equivalent to scaling the input by that constant. For example, f(x)=x, then f(2x)=2*x=2*f(x). By contrast, g(x)=x^2 is not linear since we get g(2x)=(2x)^2=4x^2 which is not equal to 2*g(x)=2*x^2. This is often referred to as homogeneity of degree 1.

2. f(x+y)=f(x) + f(y): the function of a sum of inputs is equal to the sum of the function applied to each input. This is known as superposition. For example, f(x)=x is our function, then f(1+2)=3 and f(1)+f(2)=1+2=3. Contrast with g(x)=x^2 for which g(1+2)=9 does not equal g(1)+g(2)=5.

Put it all together and you can express the requirements for linearity with one equation:
f(cx+dy)=cf(x)+df(y), where c and d are constants.

That's all there is to it. Hope that helps.