Question

A direct variation function includes the ordered pair

(4, 5). Which statement is true?
✓
The constant of variation k is
kis
The constant of variation k is
It is not possible to determine the constant of
variation from the information
given.
COMPLETE
If y varies directly with x, and y is 14 when x is 2,
what is the value of x when y is 35?
X=
DONE

Answer 1

Explanation:

For a direct variation function, the relationship between x and y can be expressed as y = kx, where k is the constant of variation.

From the given ordered pair (4, 5), we can determine the constant of variation k:

5 = k(4)

k = 5/4

The constant of variation k is 5/4.

In the second problem, we have the information y = 14 when x = 2:

14 = k(2)

k = 14/2

k = 7

Now we need to find the value of x when y = 35 using the same constant of variation k:

35 = 7x

x = 35/7

x = 5

So, the value of x when y is 35 is 5.

Answer 2

when y is 35, x is 5.

Explanation:

To solve the direct variation problem, we can use the formula y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation. We are given the ordered pair (4, 5), which means that when x = 4, y = 5. Substituting these values into the formula gives:

5 = k * 4

To solve for k, we can divide both sides by 4:

k = 5/4

So the constant of variation is k = 5/4.

To solve the second problem, we can again use the formula y = kx and substitute the given values:

14 = k * 2

To solve for k, we can divide both sides by 2:

k = 7

Now that we have the constant of variation, we can use it to find the value of x when y is 35:

35 = 7x

Dividing both sides by 7 gives:

x = 5

Therefore, when y is 35, x is 5.