Question
If y varies directly with x and y = 20.4 when x = 6, find the value of y when x = -5.
Answers
GPT-4o mini
Since \( y \) varies directly with \( x \), we can express this relationship using the equation:
\[
y = kx
\]
where \( k \) is the constant of variation.
From the information given, when \( x = 6 \), \( y = 20.4 \). We can use this to find the value of \( k \):
\[
20.4 = k \cdot 6
\]
To solve for \( k \), we divide both sides by 6:
\[
k = \frac{20.4}{6} = 3.4
\]
Now that we have the value of \( k \), we can find \( y \) when \( x = -5 \):
\[
y = kx = 3.4 \cdot (-5)
\]
Calculating this gives:
\[
y = -17
\]
Thus, the value of \( y \) when \( x = -5 \) is \(\boxed{-17}\).
\[
y = kx
\]
where \( k \) is the constant of variation.
From the information given, when \( x = 6 \), \( y = 20.4 \). We can use this to find the value of \( k \):
\[
20.4 = k \cdot 6
\]
To solve for \( k \), we divide both sides by 6:
\[
k = \frac{20.4}{6} = 3.4
\]
Now that we have the value of \( k \), we can find \( y \) when \( x = -5 \):
\[
y = kx = 3.4 \cdot (-5)
\]
Calculating this gives:
\[
y = -17
\]
Thus, the value of \( y \) when \( x = -5 \) is \(\boxed{-17}\).