Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In an inverse variation, $y = 3$ when $x = 12$ . Write an inverse variation equation that shows the relationship between $x$ and $y$ . $\newline$ Write the equation using a decimal or an integer. $\newline$ $\_\_$

View step-by-step help

View step-by-step help

Write inverse variation equations

Full solution

Q. In an inverse variation,

y = 3

when

x = 12

. Write an inverse variation equation that shows the relationship between

x

and

y

.

\newline

Write the equation using a decimal or an integer.

\newline

\_\_

Understand Inverse Variation: Understand the concept of inverse variation. $\newline$ In an inverse variation, the product of the two variables is constant. This means that as one variable increases, the other decreases proportionally. The general form of an inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation. $\newline$ We are given that $y = 3$ when $x = 12$ . We can substitute these values into the inverse variation equation to find $k$ . $\newline$ Equation: $y = \frac{k}{x}$ $\newline$ Substitute $3$ for $y$ and $12$ for $x$ : $3 = \frac{k}{12}$
Solve for $k$ : Solve for the constant of variation, $k$ . To find $k$ , multiply both sides of the equation by $12$ : $3 = \frac{k}{12}$ $3 \times 12 = k$ $k = 36$
Write Inverse Variation Equation: Write the inverse variation equation using the found constant of variation. $\newline$ Now that we have found $k$ to be $36$ , we can write the inverse variation equation as: $\newline$ $y = \frac{k}{x}$ $\newline$ $y = \frac{36}{x}$

More problems from Write inverse variation equations

Question

In a direct variation,

y = 6

x = 2

. Write a direct variation equation that shows the relationship between

x

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

Posted 5 months ago

Question

y

varies directly with

x

y = 12

x = 6

y

x = 4

\newline

Write and solve a direct variation equation to find the answer.

\newline

y =

Posted 5 months ago

Question

Which equation shows inverse variation?

\newline

\newline

(\frac{x}{36}) = y

\newline

yx = -74

Posted 5 months ago

Question

y

varies inversely with

x

y = 1

x = 4

y

x = 2

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

Posted 5 months ago

Question

What is the value of

\frac{x^{2}}{y^{4}}

x=8

y=2

Posted 5 months ago

Question

(x+4)(2 x-a)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=4

x=-4

, what is the value of

a

Posted 3 months ago

Question

(2 x+5)(-m x+9)=0

\newline

In the given equation,

m

is a constant. If the equation has the solutions

x=-\frac{5}{2}

x=\frac{3}{2}

, what is the value of

m

Posted 3 months ago

Question

(4 x+3)-(5 x-7)=a x+b

\newline

In the given equation,

b

is a constant. What is the value of

b

Posted 3 months ago

Question

y=\frac{29}{8} x-\frac{2}{3}

\newline

The given equation is graphed in the

x y

-plane. What is the slope of the line?

Posted 8 months ago

Question

a t^{2}+\frac{7}{2} t-4=0

\newline

The given equation has solutions at

t=-8

t=1

. What is the value of the constant

a

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant