find the constant of variation for each direct variation.
10y=13x
and
f(x)=4.5x
and
x+y=0
Sure! Let's solve each direct variation equation separately to find the constant of variation.
1. 10y = 13x
To find the constant of variation, divide both sides of the equation by x:
10y/x = 13x/x
10y/x = 13
Therefore, the constant of variation for the equation 10y = 13x is 13.
2. f(x) = 4.5x
In this equation, f(x) represents the dependent variable. To find the constant of variation, divide both sides of the equation by x:
f(x)/x = 4.5x/x
f(x)/x = 4.5
Therefore, the constant of variation for the equation f(x) = 4.5x is 4.5.
3. x + y = 0
This equation is not a direct variation because it is not in the form y = kx or f(x) = kx, where k represents the constant of variation.
Therefore, there is no constant of variation for the equation x + y = 0.
To find the constant of variation for each direct variation equation, we need to express each equation in the form y = kx, where k represents the constant of variation.
1) 10y = 13x:
To express this equation in the form y = kx, divide both sides of the equation by 10:
y = (13/10)x.
The constant of variation, k, is (13/10).
2) f(x) = 4.5x:
In this case, the equation is already in the form y = kx, where f(x) represents y.
The constant of variation, k, is 4.5.
3) x + y = 0:
To express this equation in the form y = kx, we need to isolate y:
y = -x.
The constant of variation, k, is -1.
So, the constant of variation for the direct variation equations are:
1) k = 13/10
2) k = 4.5
3) k = -1.