Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If $y$ varies inversely with $x$ and $y = 2$ when $x = 4$ , find $y$ when $x = 1$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

View step-by-step help

View step-by-step help

Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 2

when

x = 4

, find

y

when

x = 1

.

\newline

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

\newline

y =

_____

Define Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We need to find $k$ using the given values $y = 2$ and $x = 4$ .
Substitute Values: Substitute $y = 2$ and $x = 4$ into $y = \frac{k}{x}$ to find $k$ . $2 = \frac{k}{4}$
Solve for k: Multiply both sides by $4$ to solve for $k$ . $2 \times 4 = k$
Final Inverse Variation Equation: $k = 8$ . Now we have the inverse variation equation $y = \frac{8}{x}$ .
Find $y$ for $x=1$ : Find $y$ when $x = 1$ using the equation $y = \frac{8}{x}$ . $\newline$ $y = \frac{8}{1}$
Find $y$ for $x=1$ : Find $y$ when $x = 1$ using the equation $y = \frac{8}{x}$ . $y = \frac{8}{1}$ $y = 8$ . So when $x = 1$ , $y = 8$ .

More problems from Write and solve 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 2 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 1 month ago

Question

Which equation shows inverse variation?

\newline

\newline

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

\newline

yx = -74

Posted 2 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 1 month ago

Question

What is the value of

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

x=8

y=2

Posted 10 days 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 2 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 2 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 1 month 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 1 month 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 1 month ago