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=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
.
When x equals 22 , y equals 242 .

When x=22
, y=110
.

1 answer

In direct variation, we express the relationship between \( y \) and \( x \) with the equation \( y = kx \), where \( k \) is the constant of variation.

  1. First, we know that \( y = 5 \) when \( x = 55 \). We can substitute these values into the equation to find \( k \):

\[ 5 = k \cdot 55 \]

Now, solve for \( k \):

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

So, the equation for the direct variation is:

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

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

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

Calculate \( y \):

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

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

The correct response is:

"When x=22, y=2."