Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If $y$ varies directly with $x$ and $y = 20$ when $x = 5$ , find $y$ when $x = 3$ . Write and solve a direct variation equation to find the answer. $\newline$ $y$ = ____

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. If

y

varies directly with

x

and

y = 20

when

x = 5

, find

y

when

x = 3

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

\newline

y

= ____

Establish direct variation equation: Establish the direct variation equation. $\newline$ Since $y$ varies directly with $x$ , the equation can be written as $y = kx$ , where $k$ is the constant of variation.
Find constant of variation: Use the given values to find the constant of variation $k$ . We are given that $y = 20$ when $x = 5$ . Substituting these values into the direct variation equation gives us $20 = k \times 5$ .
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $5$ to isolate $k$ . $\newline$ $\frac{20}{5} = \frac{(k \times 5)}{5}$ $\newline$ $k = 4$
Write equation with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 4$ , the direct variation equation is $y = 4x$ .
Find $y$ for $x=3$ : Find $y$ when $x = 3$ . $\newline$ Substitute $x = 3$ into the direct variation equation $y = 4x$ . $\newline$ $y = 4 \times 3$ $\newline$ $y = 12$

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