Answer:
b. -x + y = 0
Step-by-step explanation:
Direct variation:
Direct variation means "y varies directly as x”:
[tex]y \propto x \implies y=kx[/tex]
where k is the (non-zero) constant of variation.
To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.
Equation a
[tex]y=\dfrac{4}{3}x-2[/tex]
This is not a direct variation equation as there is an addition of -2.
Equation b
[tex]-x+y=0[/tex]
[tex]\implies y=x[/tex]
This is a direct variation equation where the constant of variation is 1.
Equation c
[tex]xy=8[/tex]
[tex]\implies y=\dfrac{8}{x}[/tex]
This is not a direct variation equation as y is inversely proportional to x.
Equation d
[tex]y=14[/tex]
This equation does not include the variable x, and so is therefore not a direct variation equation.
