Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which relationships have the same constant of proportionality between $y$ and $x$ as the equation $3y=27x$ ?

View step-by-step help

View step-by-step help

Identify direct variation and inverse variation

Full solution

Q. Which relationships have the same constant of proportionality between

y

and

x

as the equation

3y=27x

?

Identify Constant of Proportionality: Identify the constant of proportionality in the given equation. $\newline$ The given equation is $3y = 27x$ . To find the constant of proportionality, we need to solve for $y$ in terms of $x$ . $\newline$ Divide both sides by $3$ to isolate $y$ : $y = \left(\frac{27}{3}\right)x$ . $\newline$ The constant of proportionality is $\frac{27}{3}$ , which simplifies to $9$ . $\newline$ So, the constant of proportionality $(k)$ is $9$ .
Express as Ratio: Express the constant of proportionality as a ratio. $\newline$ The constant of proportionality $k$ is the ratio of $y$ to $x$ when $y$ is directly proportional to $x$ . $\newline$ Since $k = 9$ , the ratio of $y$ to $x$ is $\frac{y}{x} = 9$ .
Identify Relationships: Identify relationships with the same constant of proportionality. Any equation that can be rearranged to the form $y = kx$ , where $k = 9$ , will have the same constant of proportionality. For example, if we have an equation like $9y = 81x$ , we can divide both sides by $9$ to get $y = 9x$ , which has the same constant of proportionality as the given equation.
Check for Errors: Check for math errors. $\newline$ Review the previous steps to ensure that there are no math errors in the calculations or reasoning. $\newline$ The constant of proportionality was correctly identified as $9$ , and the relationships were correctly described based on this constant.

More problems from Identify direct variation and inverse variation

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