Question

4. If x = 20 when y = -4, find y when x = 10.

Answer 1

Is this a linear equation, @dianolove?

Answer 2

Wait, couldn't you do:
\[\begin{align}
y&=kx\\
-4&=k\times20\\
k&=\dfrac{-1}{5}
\end{align}\]

Answer 3

this is the question it asked me Suppose that x and y vary inversely. Write a function that models each inverse variation. Then use the equation to solve the problem.

Answer 4

Let's solve your equation step-by-step.
20x−4x=10
Step 1: Simplify both sides of the equation.
20x−4x=10
Simplify: (Show steps)
16x=10
Step 2: Divide both sides by 16.
16x16=1016
x=58
Answer:
x=58

Answer 5

do you under stand

Answer 6

20x−4y=10

Answer 7

*** x and y vary inversely***
means you can write the formula
\[ y = \frac{k}{x} \]

Answer 8

it is a inverse variation and your solving for y not x

Answer 9

that formula is useful if we know what "k" is.
to find k, we use the info
If x = 20 when y = -4, find y when x = 10.

Answer 10

in other words, replace x with 20 and y with -4 into the formula
\[ -4= \frac{k}{20} \]
and "solve for k"
by multiplying both sides by 20

Answer 11

can you find what k is ?

Answer 12

k is -80

Answer 13

yes, so now you know the formula (for this problem) is
\[ y = \frac{-80}{x} \]

find y when x = 10.
to find y, replace x with 10 in the formula and simplify

Answer 14

y=-8

Answer 15

yes

Answer 16

thanks phi will you keep helping me with these i got another one

Answer 17

ok

Answer 18

If x = 5 when , find y when x = 10.

Answer 19

missing some info

Answer 20

5. If x = 5 when y=-1 third , find y when x = 10.

Answer 21

do you mean if x=5 when y = \( - \frac{1}{3} \) ?

Answer 22

sorry mines will not do that but yes

Answer 23

is k -30

Answer 24

you could type it as y= -1/3

\[ y = \frac{k}{x} \\ - \frac{1}{3} = \frac{k}{5} \]
to find k, multiply both sides by 5
\[ - \frac{1}{3} \cdot 5 = \frac{k}{5}\cdot 5 \\
- \frac{1}{3} \cdot 5 = k \cdot \frac{5}{5} \\
- \frac{5}{3} = k
\]

Answer 25

-15

Answer 26

what is -15 ?

k is -5/3

Answer 27

oh i thought you said t multiply -5 into 3 , but what do you do now divide -5/3 into 10

Answer 28

you write the formula
\[ y = \frac{k}{x} \]
and it might be easier to understand if you write it this way
\[ y = k \cdot \frac{1}{x} \]
which means the same thing.

now replace k with -5/3
\[ y = - \frac{5}{3} \cdot \frac{1}{x} \]

Answer 29

find y when x = 10.
that means put in 10 for x in the formula
\[ y = - \frac{5}{3} \cdot \frac{1}{x} \\
y = - \frac{5}{3} \cdot \frac{1}{10}\]
and simplify

Answer 30

y=6

Answer 31

if you use a calculator on
\[ - \frac{5}{3} \cdot \frac{1}{10} \]
what do you get ?

Answer 32

-1/6

Answer 33

yes, y= -1/6 when x=10. It would be good to be able to do that without the calculator.
when you multiply fractions, you multiply top times top and bottom times bottom
\[ - \frac{5}{3} \cdot \frac{1}{10} = - \frac{5 \cdot 1 }{3 \cdot 10} \]
we could multiply the bottom 3*10 to get 30
\[ - \frac{5}{30} \]
and then simplify to get -1/6

or, it's easier to notice that 10 is 2*5
\[ - \frac{5 \cdot 1 }{3 \cdot 10} = - \frac{5 \cdot 1 }{3 \cdot 2 \cdot 5} \]
and notice we have a 5 up top and down below, and they simplify to 5/5 = 1
\[ - \frac{1 }{3 \cdot 2} = - \frac{1}{6} \]

Answer 34

what if x=-4/15 when y=-105,find x when y=4

Answer 35

\[ y = k \cdot \frac{1}{x} \\ -105= k \cdot \frac{1}{-\frac{4}{15}} \]

Answer 36

multiply both sides by -4/15,

Answer 37

k=28

Answer 38

so
\[y = \frac{28}{x} \]
find x when y=4
replace y with y
\[ 4 = \frac{28}{x} \]

Answer 39

first multiply both sides by x
then divide both sides by 4

Answer 40

7

Answer 41

yes.
\[ 4 x= \frac{28}{x} \cdot x \\ 4x = 28 \\\frac{4x}{4}= \frac{28}{4} \\x=7\]

Answer 42

thanks are you getting tired of me asking questions

Answer 43

no, but I do have to go. make a new post and someone will help you.

Answer 44

ok thanks