Bathroom

Bathroom
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  • Bingo! To fix this we just need to figure out how fast the bathtub is draining its water.
  • Oh No! The bathtub is draining water! When is it all going to be gone? Do you have any ideas?
  • That seems difficult. How are we going to do this? 
  • It really isn't that hard. All you have to do is use what we already know to make a linear equation. I'll help you! we can do this.
  •   Perfect! We already know that. Now we have to make an equation. To do this we need to use slope intercept form. y=mx + b. Where m=slope and b= your y intercept
  • Well I know it was draining for 40 seconds and there was 3 gallons in the tub, but now its been 60 seconds and there is now 10 gallons.When it was 50 seconds 11.5 gallons were in the tub and when 20 seconds passed there were 16 gallons
  • So in this case,  the y intercept represents the the amount of gallons in the tub before draining, and the x represents  the amount of time the tub has been draining for. Well then what is slope?
  • Slope is the common ratio of how fast the tub drains. Oh look it has now been 80 seconds and there is now only 7 gallons in the tub.
  • Ok I follow you. This is way easier then i first thought. 
  • To find slope we have todo Y2 -Y1/ X2-x1. So in this case 10-13/60-40=-3/20. See this isn't so hard. Now we have to find our Y intercept. The formula for that is B=y-mx. So first plug in any y coordinate from earlier. Well go with 10. Now we have to plug in our slope(-3/20). and then multiply that by the x coordinate from the y we used earlier. When we do that we would get 19.
  • Wow! That's crazy, thanks so much!
  • Yeah it it is isn't it! So from figuring that out we now know our equation is Y=-3/20x + 19. So for every 20 seconds the water goes down 3 gallons. That is all. Easier than you thought. 
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