# write an equation of direct variation  Y= 4, X= 10 y=16,x=8 y=-12,x=18 y=-5, x=15 y=2,x=2 y=-4,x=-1

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should remember that the equation of direct variation is the special case of the linear equation, such that: y = kx.

In your case, you need to find k and you need to write the equation that expresses the variation.

When x = 10 and y = 4, plug these values in the equation above such that:

4 = k*10 => k = 4/10 => k = 2/5

The equation of direct variation is y=(2/5)*x

When x = 8 and y = 16, plug these values in the equation above such that:

16 = k*8 => k =  `16/8`  => k = 2.

The equation of direct variation is y=2*x

When x = 18 and y = -12, plug these values in the equation above such that:

-12 = k*18 => `k = -12/18 = -2/3`  The equation of direct variation is `y=-(2/3)*x`

When x = 15 and y = -5, plug these values in the equation above such that:

-5 = k*15 => k = `-5/15`  = `-1/3`

The equation of direct variation is `y=-(1/3)*x`

When x = 2 and y = 2, plug these values in the equation above such that:

2 = k*2 => k = 1

The equation of direct variation is y=x

When x = -1 and y = -4, plug these values in the equation above such that:

-4 = -k*1 => k =4

The equation of direct variation is y=4x

The equations of direct variation are: `y=(2/5)*x ; y=2*x ; y=-(2/3)*x ; y=-(1/3)*x ; y=x ;y=4x` .