Respuesta :
Answer:
b. [tex]2x-3y=0[/tex]
d.[tex]x=-0.25y[/tex]
Step-by-step explanation:
Direct variation refers to a relationship between two variables such that when one variable changes, the other changes proportionally.
Mathematically, if two variables x and y are in direct variation, it means that y is directly proportional to x and can be expressed as:
[tex]y = kx[/tex]
where
- k is the constant of variation.
To determine which of the given equations represent direct variation, we need to rewrite each equation in the form y = kx and observe if y is directly proportional to x with a constant of variation k.
Let's analyze each equation:
a. [tex]x - y = 1[/tex]
This equation is not in the form [tex]y = kx[/tex], so it does not represent direct variation.
b. [tex]2x - 3y = 0[/tex]
Rearranging the equation, we get:
[tex]3y = 2x[/tex]
[tex]y = \frac{2}{3} x[/tex]
This equation is in the form [tex]y = kx[/tex], so it represents direct variation with [tex]k=\frac{2}{3}[/tex]
c. [tex]xy = 0[/tex]
This equation represents a product of x and y equal to zero, but it does not represent direct variation.
d. [tex]x = -0.25y[/tex]
Rearranging the equation, we get:
[tex]y = -4x[/tex]
This equation is in the form [tex]y = kx[/tex], so it represents direct variation with [tex]k = -4[/tex]
e. [tex]x = 1[/tex]
This equation represents a constant value of x, but it does not represent direct variation.
f. [tex]y = -x + 4[/tex]
This equation is in the form [tex]y = kx[/tex] where [tex]k=-1[/tex], but it is not a direct variation because y is not directly proportional to x.
So, the equations of direct variation are:
b. [tex]2x - 3y = 0[/tex]
d. [tex]x = -0.25y[/tex]
