6y-x=1
Tell weather x and y show direct variation. Explain your reasoning. If so, find k. Show your work.
(Y=kx)
"whether"
Not direct variation.
That "1" queers the deal.
In other words, the equation is NOT just y=kx.
To determine if the variables x and y show direct variation, we need to check if their relationship can be expressed in the form y = kx, where k is a constant.
In this case, we have the equation 6y - x = 1. To see if it can be rewritten in the form of direct variation (y = kx), let's rearrange the equation:
6y - x = 1
6y = x + 1 (add x to both sides)
y = (1/6)x + 1/6 (divide both sides by 6)
From the final equation, we can see that the relationship between x and y indeed follows the form y = kx, with k = 1/6. Therefore, x and y show direct variation, and the constant of variation (k) is equal to 1/6.
To summarize:
The variables x and y show direct variation because their relationship can be expressed as y = kx, where k = 1/6.