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)%0D%0AResponses%0D%0A%0D%0AWhen x=22, y=242.%0D%0AWhen x equals 22 , y equals 242 .%0D%0A%0D%0AWhen x=22, y=110.%0D%0AWhen x equals 22 , y equals 110 .%0D%0A%0D%0AWhen x=22, y=111.%0D%0AWhen x equals 22 , y equals Start Fraction 1 over 11 End Fraction .%0D%0A%0D%0AWhen x=22, y=2

Answer 1

To find the direct variation equation, we start with the formula for direct variation:

\[ y = kx \]

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

From the information provided, we know that \( y = 5 \) when \( x = 55 \). We can use this to find \( k \):

\[ 5 = k \cdot 55 \]

Now, solving for \( k \):

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

Now we can write the direct variation equation:

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

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

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

Calculating this, we get:

\[ y = 2 \]

So the answer is:

When x=22, y=2.