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 first need to establish the equation for direct variation. If \( y \) varies directly with \( x \), we can express this relationship as:

\[
y = kx
\]

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

Given \( y = 5 \) when \( x = 55 \), we can find \( k \):

\[
5 = k \cdot 55
\]

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

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

Now that we have \( k \), 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 gives:

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

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

The correct response is:

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

or

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