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 [tex]x[/tex] and [tex]y[/tex] are in direct variation, it means that [tex]y[/tex] is directly proportional to [tex]x[/tex] and can be expressed as:
[tex]y = kx[/tex]
where
To determine which of the given equations represent direct variation, we need to rewrite each equation in the form [tex]y = kx[/tex] and observe if [tex]y[/tex] is directly proportional to [tex]x[/tex] with a constant of variation [tex]k[/tex].
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 = \dfrac{2}{3}x[/tex]
This equation is in the form [tex]y = kx[/tex], so it represents direct variation with [tex]k = \dfrac{2}{3}[/tex].
c. [tex]xy = 0[/tex]
This equation represents a product of [tex]x[/tex] and [tex]y[/tex] 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 [tex]x[/tex], 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 [tex]y[/tex] is not directly proportional to [tex]x[/tex].
So, the equations of direct variation are:
b. [tex]2x - 3y = 0[/tex]
d. [tex]x = -0.25y[/tex]
