Question

Write and solve the equation for the direct variation y varies directly with x if y=5 when x=55. Then find the value of y when x=22.(1 point)
Responses

When x=22, y=110.
When x equals 22 , y equals 110 .

When x=22, y=2.
When x equals 22 , y equals 2 .

When x=22, y=111.
When x equals 22 , y equals Start Fraction 1 over 11 End Fraction .

When x=22, y=242.

Answer 1

To solve for the direct variation where \( y \) varies directly with \( x \), we use the formula:

\[ y = kx \]

where \( k \) is the constant of variation.

We are given that \( y = 5 \) when \( x = 55 \). We can solve for \( k \):

\[ 5 = k(55) \]

To find \( k \), we can divide both sides by 55:

\[ k = \frac{5}{55} = \frac{1}{11} \]

Now we have the equation of direct variation:

\[ y = \frac{1}{11} x \]

Next, we need to find the value of \( y \) when \( x = 22 \):

\[ y = \frac{1}{11} \times 22 \]

Calculating this gives:

\[ y = \frac{22}{11} = 2 \]

So, when \( x = 22 \), \( y = 2 \).

The correct response is:

**When x=22, y=2.**
**When x equals 22 , y equals 2.**