Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The following table shows a proportional relationship between $x$ and $y$ . $y$ : $2$ $5$ $8$ $x$ : $9$ $22.5$ $36$ Write an equation to describe the relationship between $x$ and $y$ .

View step-by-step help

View step-by-step help

Write inverse variation equations

Full solution

Q. The following table shows a proportional relationship between

x

and

y

.

y

:

2

5

8

x

:

9

22.5

36

Write an equation to describe the relationship between

x

and

y

.

Identify Proportionality Constant: Now that we have the constant of proportionality, we can write the equation that describes the relationship between $x$ and $y$ . The general form of the equation for a proportional relationship is $y = kx$ . Substitute the value of $k$ into the equation. $y = \frac{2}{9}x$
Write Proportional Relationship Equation: To ensure that we have not made a math error, we can check our equation with another pair of values from the table. Let's use the second pair $(y = 5, x = 22.5)$ . $\newline$ Substitute $x = 22.5$ into the equation $y = \frac{2}{9}x$ . $\newline$ $y = \frac{2}{9} \times 22.5$ $\newline$ $y = 5$ $\newline$ Since the result matches the y-value given in the table for $x = 22.5$ , our equation is correct.

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 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