Question
The variable \( y \) varies inversely with \( x \). Write an inverse variation equation that relates \( x \) and \( y \). Then find the missing value of \( x \) or \( y \). 19. When \( x=6, y=2 \). Find \( x \) when \( y=1 \).
Ask by Little Marshall. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The inverse variation equation is \( y = \frac{12}{x} \). When \( y = 1 \), \( x = 12 \).
Solution
1. We are told that \( y \) varies inversely with \( x \), which means the relation can be written as
\[
y = \frac{k}{x},
\]
where \( k \) is a constant.
2. Using the values \( x = 6 \) and \( y = 2 \), we can substitute into the equation to find \( k \):
\[
2 = \frac{k}{6}.
\]
Multiplying both sides by 6 gives:
\[
k = 12.
\]
3. Now the inverse variation equation is:
\[
y = \frac{12}{x}.
\]
4. To find \( x \) when \( y = 1 \), substitute \( y = 1 \) into the equation:
\[
1 = \frac{12}{x}.
\]
Multiply both sides by \( x \) to obtain:
\[
x = 12.
\]
Thus, when \( y = 1 \), the value of \( x \) is \( 12 \).
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Simplify this solution Bonus Knowledge
The relationship of inverse variation can be expressed with the equation \( y = \frac{k}{x} \), where \( k \) is a constant. Given that \( x = 6 \) and \( y = 2 \), we can solve for \( k \) by substituting the values: \( 2 = \frac{k}{6} \) which gives us \( k = 12 \). Therefore, our inverse variation equation becomes \( y = \frac{12}{x} \). Now, to find \( x \) when \( y = 1 \), we set up the equation: \( 1 = \frac{12}{x} \). Solving for \( x \) gives us \( x = 12 \). So, when \( y = 1 \), the corresponding value of \( x \) is \( 12 \).
