Does the equation 7x-4y=0 represent a direct variation? If so, find the constant of variation.
A) yes; k= 7/4
B) yes, k=-4
C) No ( i think c)
D) yes; k=-7/4
If you have an equation of the form y = mx + b, and b = 0
then you have a direct variation
So for yours:
7x-4y=0
-4y = -7x
y = (7/4)x , no b value, so .....
To determine if the equation represents a direct variation, we need to check if it can be written in the form y = kx, where k is the constant of variation.
Starting with the given equation: 7x - 4y = 0, let's isolate y.
First, subtract 7x from both sides of the equation:
-4y = -7x
Next, divide both sides of the equation by -4 to solve for y:
y = (7/4)x
Comparing this equation to the form y = kx, we can see that k = 7/4.
Therefore, the equation 7x-4y = 0 represents a direct variation, and the constant of variation is k = 7/4.
So, the correct answer is A) yes; k = 7/4.
To determine if the equation 7x - 4y = 0 represents a direct variation, we need to check if it can be written in the form y = kx, where k is a constant of variation.
First, let's manipulate the equation to isolate y on one side. Start by adding 4y to both sides:
7x - 4y + 4y = 0 + 4y
Simplifying, we have:
7x = 4y
To isolate y, divide both sides of the equation by 4:
(7x)/4 = (4y)/4
Simplifying again:
7x/4 = y
Now, we can rewrite the equation in the form y = kx, where k is the constant of variation:
y = 7x/4
Comparing this to the form y = kx, we see that the equation 7x - 4y = 0 does represent a direct variation. The constant of variation, k, in this case, is 7/4.
Therefore, the correct answer is A) yes; k = 7/4.