Tell if x and y show direct variation. Explain reasoning.
1) x=2y
2) y-x=6
3) xy=5
direct: y=kx or x=ky
inverse: xy = k
where k is a constant.
So, check 'em out.
back
To determine if x and y show direct variation, we need to check if they have a constant ratio. Here's how we can verify it for each given equation:
1) x = 2y
To determine if x and y show direct variation, we can rewrite the equation in the form y = kx, where k is a constant. From the given equation, we can rearrange it to be y = (1/2)x. Since we can represent y as the constant times x, we can conclude that x and y show direct variation.
2) y - x = 6
In this equation, we do not have a constant ratio since there is a constant term (6) involved. Therefore, x and y do not show direct variation.
3) xy = 5
Similar to the previous equation, this equation doesn't have a constant ratio since there is multiplication involved. Thus, x and y do not show direct variation.
To summarize:
- Equation 1 (x = 2y) shows direct variation because it can be rewritten as y = (1/2)x.
- Equations 2 (y - x = 6) and 3 (xy = 5) do not show direct variation because they involve terms other than a constant ratio between x and y.