I don't know how i got this question wrong.
In a direct variation, the constant of proportionality is -3.
Which of the following would be its equation?
A) y = x - 3
B) -3y = x
C) y = -3x
D) -3 = xy
I put A as my answer... but it says the answer is C! How is C the answer?
PLZ keep ur explanation simple.
Thanks for helping me,
Scar
direct variation means y is proportional to x
(if you double x, you double y)
algebraically that means;
y = k * x where k is a constant which they call "constant of proportionality" and I just call "k" :)
here
y = (-3) * x or -3x
thnx Damon 😊
You are welcome.
In a direct variation, the equation is of the form y = kx, where k represents the constant of proportionality. In this case, the constant of proportionality is -3. So the correct equation would be y = -3x. Let me explain why:
To solve this problem, recall that in a direct variation, the ratio of y to x is always constant. In other words, if we divide y by x, the result will always be the same. In this case, the ratio is -3 because the constant of proportionality is -3.
So, let's test each answer choice and see which one satisfies this condition:
A) y = x - 3
If we divide y by x, we get (x - 3)/x, which is not a constant. So A is incorrect.
B) -3y = x
If we divide -3y by x, we get (-3y)/x = -3(y/x). Since y/x is not constant, this equation does not represent a direct variation. So B is incorrect.
C) y = -3x
If we divide y by x, we get (-3x)/x = -3. Since -3 is constant, this equation represents a direct variation. So C is correct.
D) -3 = xy
If we divide -3 by xy, we get (-3)/(xy), which is not a constant. So D is incorrect.
Therefore, the correct equation representing the direct variation with a constant of proportionality -3 is y = -3x, which is option C.