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  • 1.)Hey Julia how long is it going to be until you're done in here?
  • 2.) I'm not sure but we can find out.
  • 2.) The independent variable or the x value of this problem is the time in seconds the tub has been draining. The dependent variable or y value of this problem is the gallons left in the tub.
  • 1.) When I pulled the plug from the bath tub and waited 40 seconds there was 13 gallons left in the tub. After waiting a total of 60 seconds there was 10 gallons left in the tub. To figure this problem out we will use the expression y=mx+b
  • 3.) Based on this information you have the ordered pairs (40,13) and (60, 10). With this you take the x and y values of this problem and subtract them from each other (10-13/60-40) to get the m. m=-3/20
  • 4.) What about b.
  • 2.) The b in the expression y=mx+b is the y intercept which is the amount that was in the before it started draining. m is the slope, slope is the is the rate of change and our slope is -3/20 which represents the amount the tub drains in a certain amount of time (x).
  • 1.) To find b you must substitute a set of ordered pairs in for the x and y values (40,13) and -3/20 in for m and then just slove for b. 13=-3/20(40)+b, 13=-6+b, 19=b.
  • 3.) The x intercept of this problem is 126.7 which means it takes 126.7 seconds for the tub to drain.
  • 4.)How much water was in the tub after 20 seconds? 50 seconds?
  • 1.) To find how much water is in the tub at a certain time you sub the time in for x and solve for y. So y=-3/20(20)+19, y=-3+19, y=16. And for 50 seconds it would be y=-3/20(50), y=-7.5+19, y=11.5.
  • 2.)How long will it take until there is 7 gallons left in the tub? How long will it take the tub to empty?
  • 1.)To find how long it takes for the tub to have a certain amount of water in it you substitute the number of gallons in for y and then solve for x. So 7=-3/20x+19, -12=-3/20x, x=80. Then for the amount of time it takes for the tub to drain (the x intercept) 0=-3/20x+19, -19=-3/20x, x=126.7.
  • 2.) Thanks for teaching me! Now... can i use the bathroom?
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