How Did the Equation Change to y = x + 30?

AI Thread Summary
The discussion revolves around the transformation of the equation from 5x + 2(30) = y to y = x + 30. Participants express confusion about how the linear equation y = 5/3x + 20 relates to y = x + 30. Clarifications indicate that the transition to y = x + 30 likely stems from an additional condition not included in the original problem statement. There is also a correction regarding the interpretation of the equations, emphasizing that dividing through by 3 leads to a different form. The conversation highlights the importance of understanding the context and conditions surrounding the equations.
nukeman
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**Quick: Just a SIMPLE question on Linear equation.

Homework Statement



Ok,

5x + 2(30) = y

turns into:

5/3x + 20 = y (that is 5 over 3 x)

Now it says something I don't understand.

"We now have two equations:

y = 5/3x + 20 and y = x + 30 (How did it get y = x + 30?)



Homework Equations





The Attempt at a Solution



Thanks, appreciate it!
 
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nukeman said:

Homework Statement



Ok,

5x + 2(30) = y

turns into:

5/3x + 20 = y (that is 5 over 3 x)

I don't understand this, your book went from a linear line to a non-linear line?
 


nukeman said:

Homework Statement



Ok,

5x + 2(30) = y

turns into:

5/3x + 20 = y (that is 5 over 3 x)
Perhaps you mean (5/3)x+ 20= y but even that is wrong. Dividing 5x+ 2(30)= y through by 3 gives (5/3)x+ 20= (1/3)y.

Now it says something I don't understand.

"We now have two equations:

y = 5/3x + 20 and y = x + 30 (How did it get y = x + 30?)
Presumably y= x +30 is given by some other condition before what you have quoted.



Homework Equations





The Attempt at a Solution



Thanks, appreciate it!
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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