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, where x represents the number of weeks that have passed and y represents the height of the plant at the end of each week. They want to use the equation to estimate when the height of the plant will be 10 inches. Amalia's estimate is after 6 weeks, and Alec's estimate is after Week 15. Is either student correct? Explain.
so im doing a test and i need help
well, you want
2.5 + 1.25x = 10
so, just solve for x
To determine if either student's estimate is correct, we can substitute the value of 10 inches into the equation y = 2.5 + 1.25x and solve for the value of x.
Let's start with Amalia's estimate of 6 weeks:
y = 2.5 + 1.25x
10 = 2.5 + 1.25(6)
10 = 2.5 + 7.5
10 = 10
Amalia's estimate is correct. At the end of 6 weeks, the height of the plant will be approximately 10 inches.
Now let's check Alec's estimate of 15 weeks:
y = 2.5 + 1.25x
10 = 2.5 + 1.25(15)
10 = 2.5 + 18.75
10 = 21.25
Alec's estimate is not correct. At the end of 15 weeks, the estimated height of the plant will be approximately 21.25 inches, not 10 inches.
To determine if either student's estimate is correct, we can substitute the value of 10 for y in the equation y = 2.5 + 1.25x and solve for x.
For Amalia's estimate of 6 weeks, the equation becomes:
10 = 2.5 + 1.25(6)
10 = 2.5 + 7.5
10 ≠ 10
For Alec's estimate of 15 weeks, the equation becomes:
10 = 2.5 + 1.25(15)
10 = 2.5 + 18.75
10 ≠ 20.25
From these calculations, we see that neither estimate is correct.
To accurately estimate when the height of the plant will be 10 inches, we need to set y = 10 in the equation and solve for x:
10 = 2.5 + 1.25x
Subtracting 2.5 from both sides, we get:
7.5 = 1.25x
Dividing both sides by 1.25, we obtain:
x = 6
So the correct estimate is that the height of the plant will be 10 inches after 6 weeks.