WRITE A DIRECT VARIATION EATION THAT RELATES THE TWO VARIABLES

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

Problem 1 :

x = 4, y = 8

Solution :

Equation of direct variation is y = kx

8 = k(4)

8/4 = k

2 = k

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

To find y :

y = 2x

Substitute the value of x.

y = 2(12)

y = 24

So, the value of y is 24 when x = 12.

Problem 2 :  

x = -3, y = -5

Solution :

The equation is in the form y = kx

-5 = k(-3)

-5/-3 = k

5/3 = k

So, the equation that relates x and y is y = 5/3x.

To find y :

y = (5/3)x

Substitute the value of x.

y = 5/3(12)

y = 20

So, the value of y is 20 when x = 12.

Problem 3 :

x = 35, y = -7

Solution :

The equation is in the form y = kx

-7 = k(35)

-7/35 = k

-1/5 = k

So, the equation that relates x and y is y = -1/5x.

To find y :

y = -1/5x

Substitute the value of x.

y = -1/5(12)

y = -12/5

y = -2.4

So, the value of y is -2.4 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 1 :

x = 5, y = -15

Solution :

The equation is in the form y = kx

-15 = k(5)

-15/5 = k

-3 = k

So, the equation that relates x and y is y = -3x.

To find x :

y = -3x

Substitute the value of y.

-4 = -3x

-4/(-3) = x

4/3 = x

1.33 = x

So, the value of x is 1.33 when y = -4

Problem 2 :

x = -6, y = 8

Solution :

The equation is in the form y = kx

8 = k(-6)

8/-6 = k

-4/3 = k

So, the equation that relates x and y is y = -4/3x.

To find x :

y = -4/3x

Substitute the value of y.

-4 = -4/3x

-4 × (-3/4) = x

3 = x

So, the value of x is 3 when y = -4

Problem 3 :

x = -18, y = -2

Solution :

The equation is in the form y = kx

-2 = k(-18)

-2/-18 = k

1/9 = k

So, the equation that relates x and y is y = 1/9x.

To find x :

y = 1/9x

Substitute the value of y.

-4 = 1/9x

(-4) × 9 = x

-36 = x

So, the value of x is -36 when y = -4.