The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y.

y=72; x=3

y = kx

Replace y and x to solve for k:

72 = 3k

Divide both sides by 3:

k = 24

Now replace k with 24:

y = 24x

The proportionality constant [tex]k=\frac{1}{24}[/tex], and the equation that relates [tex]x[/tex] and [tex]y[/tex] is [tex]x=\frac{1}{24}y\text{ or } y=24x[/tex]

Since [tex]x[/tex] and [tex]y[/tex] are related by direct proportion,

[tex]x \text{ }{\displaystyle \propto}\text{ }y \implies x=ky[/tex]

where [tex]k[/tex] is our proportionality constant. To find the value of [tex]k[/tex], substitute the values [tex]x=3\text{ and } y=72[/tex] into the formula, and solve for [tex]k[/tex].

[tex]x=ky\\\implies 3=72k\\\implies k=\frac{1}{24}[/tex]

Thus the equation that relates [tex]x[/tex] and [tex]y[/tex] is

[tex]x=\frac{1}{24}y\text{ or } y=24x[/tex]

Learn more about direct proportion here: https://brainly.com/question/908424

You earn $56 walking your neighbor's dog for 8 hours. Your friend earns $36 painting your neighbor's fence for 4 hours.
What is your pay rate? And What is your friend's pay rate?

I need help!! Please ASAP! will mark brainliest

You can solve the following proportion by cross multiplying. What will the equation be after you cross multiply?

3/9 = x/15

use the distributive property to expand expressions.
4(9x + 3y)

Mary and Julie both have a goal of raising $1000 for
charity. Mary raises $12 every 4 days. Julie raises $19
every 6 days.
Will Mary or Julie reach her goal first? Explain.

This is the sample response… Mary would have a rise of 12 and a run of 4, making her slope, or rate of change, $3 a day. Julie would have a rise of 19 and a slope of 6, making her slope, or rate of change, $3.17 a day. Since Julie is raising money at a faster rate, she would get to the goal of $1000 first.

This is the info that you should include in your response… Mary has a rise of 12 and a run of 4. Mary has a slope of 3. Julie has a rise of 19 and a run of 6. Julie has a slope of 19/6 or 3 and 1/6. Julie will reach her goal first, as she has the greater slope.

Use this information at your advantage.
Hope this helps! :))

oh lord help :,) please and thank you

please answer the question on the picture

I need help
I know I should know but I don´t know it

A hot air balloon is at elevation of 650 feet. After it descends 120 feet, what is the elevation of the balloon?

Use the table that shows the prices of different amounts of mixed fruit at the grocery store. Please help

Step 8: Does the direction of the graphed line correspond to the sign of the calculated slope?
-Cannot determine, because the function is neither increasing nor decreasing.
-Yes, because the graph line points up and right and has a positive slope.
-No, because the graph line points down and right and has a positive slope.
-No, because the graph line points up and right and has a negative slope.
-Yes, because the graph line points down and right and has a negative slope.

Complete the table using the equation y = 4x + 8.

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Does the table represent a proportional or a nonproportional linear relationship?

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Read the following statement: Line segment CD is congruent to line segment XY.

Which of the following is an equivalent statement?

A) CD overbar is similar to XY overbar
B) CD overbar is congruent to XY overbar
C) CD overbar equals XY overbar
D) CD overbar is an element of XY overbar

HELP ME OUT WITH THIS MATH QUESTION

Help MMEEEE PLKEASEEss.

HELP ME PLZ
1. If the venue needs to sell 86 tickets to break even, then how much money have they invested in the concert.

2. Desribe how you know that this is a propornational realainship.

3. What does the ordered pair (6,204) represent in this situation.

Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert units of measurement?

Write three to four sentences.

What is the value of x

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Ms. Hassan plans to serve appetizers at her Christmas party. She plans on offering 8 appetizers for every 3 people. If she has 240 people RSVP to the Christmas party, then how many appetizers will she serve?

Write an equation for the trend line shown

pls go do another problem if u dont know how tod this....... Simplify −9+1/4x−6−1/8x show your work

Martin is comparing two different video game stores.


*At Best Buy, the equation c=59.99g


*At PC Richard & Son, the cost of 2 games is $117.96, and the cost of 5 games is $294.90


How much money, per game would Martin save by going to the less expensive gas station?

If you don’t know plz don’t answer it :))

i need help ! please asap!!!!

can someone help me with this ASAP

Rectangle WXYZ with vertices W(-1,4), X(-1,1), Y(5,1), and Z(5,4). What is the perimeter?
HELP PLEASE I WILL GIVE BRAINLIEST TO BEST ANSWER AND 20 POINTS!!!!

If a number and a variable are together with no sign between them, what operation does that show?

What is the equation of the line that passes through the point (4,-2)(4,−2) and has a slope of -2−2?
(will give bainlist)