# How to know if there is an inverse or direct relation

• isukatphysics69
In summary, the conversation discusses determining the exponent and coefficient of a power law that best fits data, as well as whether the acceleration is directly or inversely proportional. The slope and y-intercept are calculated, and it is determined that the function is not exponential. There is confusion about determining direct or inverse proportionality based on log log and normal graphs, but it is eventually realized that it is determined by the relationship between multiplication and division.
isukatphysics69

## Homework Equations

log(y) = mlog(x)+log(k)
y=kxm

## The Attempt at a Solution

Determine the exponent m and coefficient k of the power law that best fits your data. Is the acceleration directly or inversely proportional?

Taking some points on the graph to get the slope
(0.78 - 0) / (2.28 - 1.52) = 1.026315789 = slope
finding the y intercept
y = mx + b
b = -mx + y
when y is 0 x is 1.52 so
b = -1.026315789*1.52 = -1.559999999

Now to the question
k = 10-1.559999999 = 0.02754228
m = 101.026315789 = 10.6246783
function is now
0.02754228*x10.6246783]

This looks like an exponential function. So on the log log graph it looks linear and on the normal graph it looks exponential. I am unsure how to determine if that is inversely or directly proportional. I am thinking inversely.

#### Attachments

• loglog.jpg
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Google is your friend on this one, it has over 1 000 000 answers for directly and inversely proportional.
After all, part of learning is learning to find things.

isukatphysics69 said:

## Homework Statement

View attachment 225004

## Homework Equations

log(y) = mlog(x)+log(k)
y=kxm

## The Attempt at a Solution

Determine the exponent m and coefficient k of the power law that best fits your data. Is the acceleration directly or inversely proportional?

Taking some points on the graph to get the slope
(0.78 - 0) / (2.28 - 1.52) = 1.026315789 = slope
finding the y intercept
y = mx + b
b = -mx + y
when y is 0 x is 1.52 so
b = -1.026315789*1.52 = -1.559999999

Now to the question
k = 10-1.559999999 = 0.02754228
m = 101.026315789 = 10.6246783 wrong.
function is now
0.02754228*x10.6246783]

This looks like an exponential function. So on the log log graph it looks linear and on the normal graph it looks exponential. I am unsure how to determine if that is inversely or directly proportional. I am thinking inversely.
You denoted the slope by m, and calculated it as m=1.026. The original function is a=k*xm. This is not an exponential function.

isukatphysics69
ehild said:
You denoted the slope by m, and calculated it as m=1.026. The original function is a=k*xm. This is not an exponential function.
Ok i think i see, the slope of the log log graph is actually the power of the "normal" graph

0.02754228*x1.026315789]
Graphing this give a straight line. So is it correct to say that direct proportionality will be determined by linear growth in both log log graph and "normal" graph

Thinking about this i don't think so, there may be graphs where there are curves but an underlying power law relation.

Wow i am a complete moron. i have figured out this lab report. It has nothing to do with transitioning from log graph to normal graph it is just a matter direct (multiplication) or inverse (division) relationships. i was thinking there is some kind of relation between log log graphs and normal graphs that will determine inverse or direct idk what on Earth i was thinking wow
like once you convert graphs there will be a way to tell a certain relationship idk where i got this idea in my head

## 1. What is an inverse relation?

An inverse relation is a mathematical relationship where the input and output values are reversed. In other words, as the input value increases, the output value decreases.

## 2. How do you determine if a relation is direct or inverse?

A direct relation is one where the input and output values increase or decrease at the same rate. An inverse relation, on the other hand, has input and output values that change in opposite directions. To determine the type of relation, you can plot the data on a graph and see if it forms a straight line or a curved line.

## 3. What is the difference between an inverse and a direct relation?

The main difference between an inverse and a direct relation is the way the input and output values change. In a direct relation, they change in the same direction, while in an inverse relation, they change in opposite directions.

## 4. Can a relation be both inverse and direct?

No, a relation can only be either inverse or direct. If the input and output values change in opposite directions, then it is an inverse relation. If they change in the same direction, then it is a direct relation.

## 5. How does knowing the type of relation help in solving problems?

Knowing the type of relation can help in solving problems by giving insight into how the input and output values are related. This information can be used to make predictions, find missing values, and solve equations.

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