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.
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.
Answers
GPT-4o mini
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.**
\[
y = kx
\]
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.**