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Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5 + 1.25rMULTIPLE CHOICE Question 7 Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y= 2.5 + 1.25x

X = the number of weeks that have passed


= the height of the plant
They want to use the equation to estimate when the height of the plant will be 10
Amalia's estimate is after 6 weeks.
Alec's estimate is after Week 15.
Is either student correct?

Sagot :

Amalia would be correct. They are guessing when the height would be 10, and you are given an equation that will 'predict' that. Height is y, so substitute 10 in the equation and solve for x. You will get x=6
Yes, Amalia is correct. If y=height of plant and x=number of weeks that have passed then you plug in the numbers, we are looking for height of 10 so y=10 so 10=2.5+1.25(6) is the equation if we plug in Amalias guess of 6 weeks, if we plug in Alexs guess it would be same but use his guess 15 instead of 6. So to figure out of the equation is correct I’ll replace 10 for y so I can do it out y=2.5+1.25(6) now easily solve for y by doing 1.25x6=7.5 then I add 2.5+7.5=10, so I plug 10 back in for y and it looks like 10=10 so yes she is right. But I double check by also doing the second students guess, right away I multiply 1.25x15 and I get a number larger than 10, I think it was 18 something so I know that’s wrong without even having to finish it by adding 2.5 because then it’ll only get bigger but for fun you add it say it’s 20.5 then plug 10 back in for y 10=20.5 nope they aren’t equal so answer is not right. If you want to guess for any other height, just plug it in for the y and your guess for number of weeks for x and do out the equation (I used a calculator to multiply since they aren’t whole numbers it’s easier to do 1.25x6 or whatever number on calculator I can’t do it in my head) and then just add 2.5 either with calculator or not it’s easy enough to do it in your head. Hope that helps.
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