Question

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

Answer 1

Yes, k=-2 and y=-2x

Explanation:

Using (1,-2) and (3,-6)

`k=(-6--2)/(3-1)=-2`

This implies that

y=-2x

check for the 3rd point;

When x=5,

y=-2(5)=-10

Hence y varies directly as x. The constant of variation is k=-2

Answer 2

The answer is yes , k = -2 and y = -2x ⇒ first answer

Explanation:

* To prove the variation

- Check the constant change in the values of x and y

- Lets check that from the table

# At x = 1 ⇒ y = -2

# At x = 3 ⇒ y = -6

# At x = 5 ⇒ y = -10

* -6 - -2 = -6 + 2 = -4 ⇒ 3 -1 = 2

-10 - -6 = -10 + 6 = -4 ⇒ 5 - 3 = 2

∴ y decreased by 4 when x increased by 2

* This is a constant change

∴ y is varies directly with x

∴ y ∝ x

∴ y = k x ⇒ where k is the constant of the variation

* Lets find the value of k

- You can use one value of x and y from the table

∵ x = 3 and y = -6

∴ -6 = k (3) ⇒ divide two sides by 3

∴ k = -2

∴ The equation of the variation is = y = -2x

* The answer is yes , k = -2 and y = -2x