"The quantity z varies directly with y and inversely with x. When y = –12 and x = –4, z = –36. What is the equation of variation? Write your answer in the form A or (A)/(B), where A and B are constants or variable expressions. Remember to include the value of k, the constant of variation, in exact form. z = ______ "

Write Variation Equation: Since z varies directly with y and inversely with x, the equation of variation can be written as z = k*(y/x), where k is the constant of variation.Substitute Given Values: We are given that when y = –12 and x = –4, z = –36. We can substitute these values into the equation to find k: –36 = k*(-12/-4).Simplify Equation: Simplifying the equation, we get –36 = k*3.Solve for k: Now, we solve for k by dividing both sides by 3: k = –36 / 3.Find Value of k: After dividing, we find that k = –12.Final Variation Equation: With the value of k found, we can write the equation of variation as z = –12*(y/x).

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The quantity $z$ varies directly with $y$ and inversely with $x$ . When $y = -12$ and $x = -4$ , $z = -36$ . What is the equation of variation? Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions. Remember to include the value of $k$ , the constant of variation, in exact form. $\newline$ $\ z$ =______

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Algebra 2

Write joint and combined variation equations II

Full solution

Q. The quantity

z

varies directly with

y

and inversely with

x

. When

y = -12

and

x = -4

z = -36

. What is the equation of variation? Write your answer in the form

A

\frac{A}{B}

, where

A

and

B

are constants or variable expressions. Remember to include the value of

k

, the constant of variation, in exact form.

\newline

\ z

=______

Write Variation Equation: Since $z$ varies directly with $y$ and inversely with $x$ , the equation of variation can be written as $z = k\cdot\frac{y}{x}$ , where $k$ is the constant of variation.
Substitute Given Values: We are given that when $y = -12$ and $x = -4$ , $z = -36$ . We can substitute these values into the equation to find $k$ : $-36 = k\cdot(-12/-4)$ .
Simplify Equation: Simplifying the equation, we get $-36 = k \times 3$ .
Solve for k: Now, we solve for $k$ by dividing both sides by $3$ : $k = -\frac{36}{3}$ .
Find Value of k: After dividing, we find that $k = -12$ .
Final Variation Equation: With the value of $k$ found, we can write the equation of variation as $z = -12\cdot\left(\frac{y}{x}\right)$ .