How do you determine whether the equation #7x + 2y = 0# represents a direct variation and if it does, how do you find the constant of variation?

Answer 1

7x + 2y = 0 2y = -7x --> y = -7/2 *(x). This is a direct variation. The constant of variation is (-7/2).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To determine if the equation represents a direct variation, check if it can be written in the form y = kx, where k is a constant. If it can, then it represents a direct variation. In this case, rearrange the equation to isolate y, then compare it to the form y = kx. If they match, it's a direct variation. The constant of variation (k) is the coefficient of x when the equation is in the form y = kx. So, for 7x + 2y = 0, rearranging to isolate y gives y = -3.5x, indicating it's a direct variation with a constant of variation of -3.5.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To determine if the equation ( 7x + 2y = 0 ) represents a direct variation, we need to rewrite it in the form ( y = kx ), where ( k ) is the constant of variation. If the equation can be written in this form, it represents a direct variation, and ( k ) is the constant of variation.

To find the constant of variation ( k ), divide both sides of the equation by ( x ) to isolate ( y ). Then, the coefficient of ( x ) will be ( k ).

So, for the equation ( 7x + 2y = 0 ), we rearrange it to solve for ( y ):

[ 7x + 2y = 0 ] [ 2y = -7x ] [ y = -\frac{7}{2}x ]

Now, comparing it with the form ( y = kx ), we see that ( k = -\frac{7}{2} ). Therefore, the equation ( 7x + 2y = 0 ) represents a direct variation, and the constant of variation ( k ) is ( -\frac{7}{2} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7