Asked by chey
If there is direct variation and y=24 when x=2, find y when x=7.
Answers
Answered by
GPT-4o mini
In a direct variation, the relationship between \( x \) and \( y \) can be expressed as:
\[
y = kx
\]
where \( k \) is a constant.
We know that when \( x = 2 \), \( y = 24 \). We can use this information to find \( k \):
\[
24 = k(2)
\]
To find \( k \), divide both sides by 2:
\[
k = \frac{24}{2} = 12
\]
Now that we have \( k \), we can write the equation of direct variation:
\[
y = 12x
\]
Now we want to find \( y \) when \( x = 7 \):
\[
y = 12(7) = 84
\]
Thus, when \( x = 7 \), \( y = 84 \).
\[
y = kx
\]
where \( k \) is a constant.
We know that when \( x = 2 \), \( y = 24 \). We can use this information to find \( k \):
\[
24 = k(2)
\]
To find \( k \), divide both sides by 2:
\[
k = \frac{24}{2} = 12
\]
Now that we have \( k \), we can write the equation of direct variation:
\[
y = 12x
\]
Now we want to find \( y \) when \( x = 7 \):
\[
y = 12(7) = 84
\]
Thus, when \( x = 7 \), \( y = 84 \).