uppose that $$ y $$ varies inversely with $$ x $$, and $$ y=2 $$ when $$ x=10 $$. (a) Write an inverse variation equation that relates $$ x $$ and $$ y $$. Equation: (b) Find $$ y $$ when $$ x=-4 $$ $$ y=\square $$

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UpStudy AI · Accepted Answer

1. Since $$ y $$ varies inversely with $$ x $$, we can write the relationship as  
   $$
   y = \frac{k}{x},
   $$  
   where $$ k $$ is a constant.

2. Given that $$ y = 2 $$ when $$ x = 10 $$, substitute these values to determine $$ k $$:
   $$
   2 = \frac{k}{10}.
   $$
   Multiply both sides by 10:
   $$
   k = 2 \times 10 = 20.
   $$

3. The inverse variation equation is then:
   $$
   y = \frac{20}{x}.
   $$

4. To find $$ y $$ when $$ x = -4 $$, substitute $$ x = -4 $$ into the equation:
   $$
   y = \frac{20}{-4} = -5.
   $$

Thus, the answers are:

(a) Equation:  
$$
y = \frac{20}{x}
$$

(b) When $$ x = -4 $$,  
$$
y = -5.
$$
(a) The inverse variation equation is $$ y = \frac{20}{x} $$. (b) When $$ x = -4 $$, $$ y = -5 $$.

uppose that \( y \) varies inversely with \( x \), and \( y=2 \) when \( x=10 \). (a) Write an inverse variation equation that relates \( x \) and \( y \). Equation: (b) Find \( y \) when \( x=-4 \) \( y=\square \)

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