Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
x and
y are in direct proportion and
y is 8 when
x is 12, find
y when
x is 6 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $8$ when $x$ is $12$ , find $y$ when $x$ is $6$ . $\newline$ Answer: $y=$

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q. If

x

and

y

are in direct proportion and

y

is

8

when

x

is

12

, find

y

when

x

is

6

.

\newline

Answer:

y=

Write Equation for Direct Variation: Write the equation for direct variation. $\newline$ 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 know that $y = 8$ when $x = 12$ . Substitute these values into the equation to find $k$ . $8 = k \times 12$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $12$ to isolate $k$ . $\newline$ $k = \frac{8}{12}$ $\newline$ $k = \frac{2}{3}$
Write Equation with Found Value: Write the direct variation equation with the found value of $k$ . Now that we have $k = \frac{2}{3}$ , the direct variation equation is $y = \left(\frac{2}{3}\right)x$ .
Find $y$ for $x=6$ : Find $y$ when $x = 6$ using the direct variation equation. $\newline$ Substitute $x = 6$ into the equation $y = \frac{2}{3}x$ . $\newline$ $y = \frac{2}{3} \times 6$
Calculate y Value: Calculate the value of y. $\newline$ y = $2 \times 2$ $\newline$ y = $4$

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 5 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 5 months ago

Question

Which equation shows inverse variation?

\newline

\newline

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

\newline

yx = -74

Posted 5 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 5 months ago

Question

What is the value of

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

x=8

y=2

Posted 5 months 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 3 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 3 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 3 months 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 8 months 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 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant