Answer:
y = 1/6x
Explanation:
To find the equation, let's see if each option works by plugging in x into each equation.
y = –1/4x
Plug -6 into x
y = –1/4(-6)
y = 1.5
y = –1/4x doesn't work because we didn't get -1.
y = 6x
Plug -6 into x
y = 6(-6)
y = -36
y = 6x doesn't work because we didn't get -1.
y = 1/6x
Plug 1/6x into x
y = 1/6(-6)
y = -1
Let's see if the other x values work.
Plug 0 into x
y = 1/6(0)
y = 0
Plug 12 into x
y = 1/6(12)
y = 2
y = 1/6x works.
y = –2x
Plug -6 into x
y = –2(-6)
y = 12
y = -2x doesn't work because we didn't get -1.
y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.
Hope that helped and have a lovely rest of your day!