Questions: Polynomial and Rational Functions Writing an inverse variation equation Suppose that y varies inversely with x, and y=5 when x=6. (a) Write an inverse variation equation that relates x and y. Equation: (b) Find y when x=-3. y=

Polynomial and Rational Functions
Writing an inverse variation equation

Suppose that y varies inversely with x, and y=5 when x=6.
(a) Write an inverse variation equation that relates x and y.

Equation:
(b) Find y when x=-3.

y=

Transcript text: Polynomial and Rational Functions Writing an inverse variation equation Suppose that $y$ varies inversely with $x$, and $y=5$ when $x=6$. (a) Write an inverse variation equation that relates $x$ and $y$. Equation: $\square$ (b) Find $y$ when $x=-3$. \[ y= \] $\square$

Solution

Solution Steps

Step 1: Understand the Problem

The problem states that $ y $ varies inversely with $ x $. This means that the relationship between $ y $ and $ x $ can be expressed as $ y = \frac{k}{x} $, where $ k $ is a constant.

Step 2: Determine the Constant $ k $

We are given that $ y = 5 $ when $ x = 6 $. We can use this information to find the constant $ k $.

\[ y = \frac{k}{x} \implies 5 = \frac{k}{6} \]

Solving for $ k $, we multiply both sides by 6:

\[ k = 5 \times 6 = 30 \]

Step 3: Write the Inverse Variation Equation

Now that we have determined $ k = 30 $, we can write the inverse variation equation:

\[ y = \frac{30}{x} \]

Step 4: Find $ y $ When $ x = -3 $

Using the inverse variation equation $ y = \frac{30}{x} $, we substitute $ x = -3 $:

\[ y = \frac{30}{-3} = -10 \]