When you have a linear graph with a positive slope the x and y variables are said to be directly proportional, what If you have a linear graph with a negative slope? Is it inversely proportional?
by 
Anonymous
ANSWERS: 3
-
Yes. As one increases the other decreases, thus inversely proportional.
-
I thought the moderators had removed my embarrasingly incorrect answer, but it just turns out that the question is repeated. This has spurred me to look for a correct answer. In my technical field, we sometimes use the term "inversely proportional" in the situation you describe, but that is sloppy at best, and just wrong at worst. I can't find any term for the negative linear slope other than directly proportional. That term seems not to care whether the proportion is positive or negative. I would suggest the term "negatively proportional", but I can't find any mathematical source which uses it. Directly proportional is defined as y being some non-0 multiple of x, and it doesn't seem to matter if that number is positive or negative. So, for example, y = 2x and y = -2x both satisfy the definition. The equation for direct proportionality then, looks like this: y = kx, where the constant k is a rational number (whole number or fraction, positive or negative) other than 0. Inverse proportionality, which is also called reciprocal proportionality, is expressed by y = k(1/x), which is not linear.
-
Directly proportional means that as value 1 (x) increases, so does value 2 (y), at a set ratio. Direct proportion is not dependent upon positive or negative. In maths, a decrease is also known as a "negative increase". This means that the value is increasing in the negative direction. So to get from -1 to -10 you have to negatively increase your number by 9. So if y negatively increases at a set rate compared to x negatively increasing, then they would be directly proportional. Inversely proportional is the opposite. y decreases as x increases, in either the positive or negative direction.
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC