Rearranging Equations to y= mx + b

  • Thread starter Ranjan1995
  • Start date
In summary: I am not sure what you are asking. I think it is impossible to find a perfect linear fit for this data.
  • #1
Ranjan1995
7
0

Homework Statement


Graph the following charts on excel so you have a linear relationship.
Determine your x and y variables before graphing, you may have to rearrange and even recalculate some of the variables.

Angle Period (s)
0 0.95
10 0.94
20 0.97
30 1.00
40 1.03
50 1.09
60 1.14
NOTE: TEACHER SAID THAT SHE GAVE THE WRONG NUMBERS, THESE WONT WORK, JUST GIVING THEM INCASE ANYONE ASKS.

Homework Equations



T=2π√(lcosα/g)
Fixed l of 1.0 m
What is g?

The Attempt at a Solution



Firstly, I have to get rid of the square root

T^2 = 4π^2cosx/g
I removed the l since it is equal to 1 and is a constant

The problem is here already. What can I do to make it a linear function. The moment i squared the T it became a quadratic/ arc.

I KNOW it isn't much, but i am struggling for so long and can't seem to get anywhere. Sorry about that guys.
 
Last edited:
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  • #2
Ranjan1995 said:

Homework Statement


Graph the following charts on excel so you have a linear relationship.
Determine your x and y variables before graphing, you may have to rearrange and even recalculate some of the variables.

Angle Period (s)
0 0.95
10 0.94
20 0.97
30 1.00
40 1.03
50 1.09
60 1.14
NOTE: TEACHER SAID THAT SHE GAVE THE WRONG NUMBERS, THESE WONT WORK, JUST GIVING THEM INCASE ANYONE ASKS.

Homework Equations



T=2π√(lcosα/g)
Fixed l of 1.0 m
What is g?



The Attempt at a Solution



Firstly, I have to get rid of the square root

T^2 = 4πcosx/g
I removed the l since it is equal to 1 and is a constant

The problem is here already. What can I do to make it a linear function. The moment i squared the T it became a quadratic/ arc.

I KNOW it isn't much, but i am struggling for so long and can't seem to get anywhere. Sorry about that guys.

In the beginning of your problem statement, you mention x and y. But then in the equation there is no "y". Is x the independent variable in the equation? If so, what is the dependent variable?
 
  • #3
T is the dependent variable
 
  • #4
So you mean x and T rather than x and y?
 
  • #5
Yes, sorry.
 
  • #6
Well I could be wrong, but I don't think you can fit a linear equation to the T = SQRT(cos(x)) equation that you are given. Are you maybe supposed to find the best linear fit across some small interval of x?
 

FAQ: Rearranging Equations to y= mx + b

1. How do you rearrange an equation to y= mx + b?

To rearrange an equation to y= mx + b, you need to isolate the y variable on one side of the equation. This can be done by using inverse operations, such as adding or subtracting terms on both sides of the equation, or dividing both sides by a coefficient. Once the y variable is isolated, the equation will be in the form of y= mx + b.

2. What does each variable represent in the equation y= mx + b?

In the equation y= mx + b, y represents the dependent variable, or the output. M represents the slope of the line, which determines the rate of change between the x and y variables. x represents the independent variable, or the input. And b represents the y-intercept, which is the point where the line intersects the y-axis.

3. Why is it important to rearrange equations to y= mx + b?

Rearranging equations to y= mx + b allows us to easily identify the slope and y-intercept of a line, which are important for graphing and analyzing linear relationships. It also allows us to easily solve for the y variable when given a specific x value, and vice versa.

4. Can you rearrange any equation to y= mx + b?

No, not all equations can be rearranged to y= mx + b. This form is specific to linear equations, which have a constant rate of change between the x and y variables. Non-linear equations, such as exponential or quadratic equations, have different forms that cannot be rearranged to y= mx + b.

5. How can I check if I rearranged the equation to y= mx + b correctly?

To check if you have correctly rearranged the equation to y= mx + b, you can substitute different values for x and y into the equation and see if they satisfy the equation. For example, if you rearranged the equation y= 2x + 3, you can substitute x= 2 and y= 7, and see if the equation is true (7= 2(2) + 3).

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