WRITE A DIRECT VARIATION EQUATION THAT RELATES X AND Y

The variables x and y vary directly. Write an equation that relates x and y. Then find y when x = 12.

Problem 1 :

x = -18, y = 4

Solution :

The equation is in the form y = kx

4 = k(-18)

4/-18 = k

-2/9 = k

So, the equation that relates x and y is y = -2/9x.

To find y :

y = -2/9x

Substitute the value of x.

y = -2/9(12)

y = -24/9

y = -8/3

y = 2.67

So, the value of y is 2.67 when x = 12.

Problem 2 :

x = 2/3, y = -10

Solution :

The equation is in the form y = kx

-10 = k(2/3)

-10(3/2) = k

-30/2 = k

-15 = k

So, the equation that relates x and y is y = -15x.

To find y :

y = -15x

Substitute the value of x.

y = -15(12)

y = -180

So, the value of y is -180 when x = 12.

The variables x and y vary directly. Write an equation that relates x and y. Then find x when y = -4.

Problem 3 :

x = -12, y = 84

Solution :

The equation is in the form y = kx

84 = k(-12)

84/-12 = k

-7 = k

So, the equation that relates x and y is y = -7x.

To find x :

y = -7x

Substitute the value of y.

-4 = -7x

-4/-7 = x

4/7 = x

0.57 = x

So, the value of x is 0.57 when y = -4.

Problem 4 :

x = -20/3, y = -15/8

Solution :

The equation is in the form y = kx

-15/8 = k(-20/3)

-15/8 × (-3/20) = k

45/160 = k

9/32 = k

So, the equation that relates x and y is y = 9/32x.

To find x :

y = (9/32)x

Substitute the value of y.

-4 = (9/32)x

-4 × (32/9) = x

-128/9 = x

So, the value of x is -128/9 when y = -4.

Problem 5 :

x = -0.5, y = 3.6

Solution :

The equation is in the form y = kx

3.6 = k(-0.5)

(3.6) × (-1/0.5) = k

-3.6/0.5= k

-7.2 = k

So, the equation that relates x and y is y = -7.2x.

To find x :

y = (-7.2)x

Substitute the value of y.

-4 = (-7.2)x

-4 × (-1/7.2) = x

4/7.2 = x

0.56 = x

So, the value of x is 0.56 when y = -4.