Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A direct variation includes the points $(2,18)$ and $(1,n)$ . Find $n$ . Write and solve a direct variation equation to find the answer. $\newline$ $n$ = ____

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. A direct variation includes the points

(2,18)

and

(1,n)

. Find

n

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

\newline

n

= ____

Identify equation: Identify the direct variation equation. $\newline$ Direct variation means $y$ is directly proportional to $x$ , which can be represented by the equation $y = kx$ , where $k$ is the constant of variation.
Find constant of variation: Use the given point $(2,18)$ to find the constant of variation $k$ . Substitute $x = 2$ and $y = 18$ into the direct variation equation $y = kx$ . $18 = k \times 2$
Solve for k: Solve for k. $\newline$ Divide both sides by $2$ to isolate k. $\newline$ $\frac{18}{2} = k$ $\newline$ $k = 9$
Write equation with $k$ : Write the direct variation equation using the found value of $k$ . Since $k = 9$ , the direct variation equation is $y = 9x$ .
Find $n$ for $x=1$ : Use the direct variation equation to find $n$ when $x = 1$ . Substitute $x = 1$ into the equation $y = 9x$ to find $n$ . $n = 9 \times 1$ $n = 9$

More problems from Write and solve direct 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