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

When x=22
, y=242
.
When x equals 22 , y equals 242 .

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

When x=22
, y=111
.

Answer 1

To solve the problem, we start with the understanding that if \( y \) varies directly with \( x \), we can express this relationship as:

\[
y = kx
\]

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

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

\[
5 = k \cdot 55
\]

To find \( k \), we can solve for it:

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

Now, we have the equation for direct variation:

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

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

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

Calculating this gives:

\[
y = 2
\]

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

The correct response is:

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