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 $y = 15$ when $x = 5$ , find $y$ when $x = 1$ . 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 = 15

when

x = 5

, find

y

when

x = 1

. 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 proportionality.
Find constant $k$ : Use the given values to find the constant $k$ . We know that $y = 15$ when $x = 5$ . Substituting these values into the equation gives us $15 = k \times 5$ .
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $5$ to isolate $k$ . $\newline$ $\frac{15}{5} = \frac{k \times 5}{5}$ $\newline$ $k = 3$
Write equation with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 3$ , the direct variation equation is $y = 3x$ .
Find $y$ for $x=1$ : Find $y$ when $x = 1$ . Substitute $x = 1$ into the direct variation equation $y = 3x$ . $y = 3 \times 1$ $y = 3$

More problems from Write and solve direct variation equations

Question

(x-3)(a x+4)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=3

x=-2

, what is the value of

a

Posted 8 months ago

Question

3 x^{2}+a x-5=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=-5

x=\frac{1}{3}

, what is the value of

a

Posted 7 months ago

Question

a x^{2}+5 x+2=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=-2

x=-\frac{1}{2}

, what is the value of

a

Posted 8 months ago

Question

Find the average value of the function

f(x)=\frac{2}{x-11}

x=2

x=8

. Express your answer as a constant times

\ln 3

\newline

\square \ln 3

Posted 9 months ago

Question

6+\frac{4}{a}+\frac{b}{3}

a=4

b=3

Posted 3 months ago

Question

4 x-32 k x=53

\newline

In the given equation,

k

is a constant. The equation has no solution. What is the value of

k

Posted 8 months ago

Question

a_{1}=9

a_{n+1}=2 a_{n}+2

then find the value of

a_{5}

\newline

Posted 9 months ago

Question

a_{1}=4

a_{n}=5 a_{n-1}-n

then find the value of

a_{5}

\newline

Posted 9 months ago

Question

a_{1}=1

a_{n}=n a_{n-1}+4

then find the value of

a_{5}

\newline

Posted 9 months ago

Question

a_{1}=9

a_{n}=n a_{n-1}-2

then find the value of

a_{5}

\newline

Posted 9 months ago

Related topics

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