Answer:
Direct variation: y = 3x, y = (2/7)x, and -0.5x = y
Not direct variation: x = -1, y = 2.2x + 7, and y = 4
Step-by-step explanation:
We know that the equation for direct variation is y = k · x, where you can fill in for k whatever number you want.
So, let’s figure this out by looking at the equations.
Equation 1: y = 3x
We know this is a direct variation equation because it all fits together and the 3 is a substitute for the variable, k.
Equation 2: x = -1
This is not an example of direct variation because:
1) the variable by itself on one side is x, when it is supposed to be y
2) there is only one number, -1, when instead it should say, -1x.
Equation 3: y= (2/7)x
This is an example of direct variation because the 2/7 is filling in for the k, and everything else matched the direct variation equation.
Equation 4: -0.5x = y
Since it doesn’t matter on which side y is, let’s just turn the equation around to make it simpler.
Now we have:
y = -0.5x
This makes sense because we have everything a direct variation equation needs to have plus the -0.5 substituting in for the k.
Equation 5: y = 2.2x + 7
This is also not an example of direct variation because although it has practically everything that an equation with direct variation has to have, it has that extra 7 there that ruins the equation.
Equation 6: y = 4
This is not an example of direct variation because there is no variable x in here! We have a k, but not an x!
Hope this helps! :)
