Answer
The equation that represents the direct variation relationship between y and x is
y = -12x
Step-by-step explanation
We are told that y varies directly with x.
y = 48 when x = -4.
We are then told to write the equation that represents this direct variation relationship.
In mathematical terms, y varies directly with x is written as
y ∝ x
If we introduce a constant of variation, k, we can then write this relationship as
y = kx
To now fully write this relationship, we need to solve for k.
y = 48 when x = -4.
y = kx
48 = k × -4
48 = -4k
-4k = 48
Divide both sides by -4
(-4k/-4) = (48/-4)
k = -12
We can then put in the value of k obtained
y = kx
y = -12x
The equation given is
3y = 10x
Recall that variation is represented as
y ∝ x
And written as
y = kx
So, we can convert 3y = 10x into this form and establish the direct variation and obtain the value of k.
3y = 10x
Divide both sides by 3
(3y/3) = (10x/3)
y = (10x/3)
which is similar to y = kx
k = (10/3)
So, option A is correct.
Hope this Helps!!!