Answer:
a) Use the data in the table to find the rate of change in the length of baby girl Grace. (2 points)
The rate of change is 1.5 inches every two months. (0.7 inches per month)
b) Write a linear equation for the graph in point-slope form. Show your work. (2 points)
0.7x-y+17.2=0
Work: (y-y1)=m(x-x1)
(y-20)=0.7(x-4)
y=0.7x-2.8+20
y=0.7x+17.2
0.7x-y+17.2=0
c) 20-1.5= 18.5 (2 months)
18.5-1.5= 17
17 inches
Grace was 17 inches at birth. I found this out by using my data and knowing that she grew 1.5 inches every two months. So, to solve I subtracted 1.5 from 20, for that was the first data that was given, and was left with the data that the baby was 18.5 inches long at birth. I did the same procedure again, subtracting 1.5 from 18.5, and was given 17. Since 17 inches long was what was recorded at zero months, that would mean that the baby was 17 inches long at birth.
d) Based on the data, I can predict that Grace will grow about 4.2- 4.5 inches in 6 months, and be about 44 inches long. To do this, I took the known rate of change (1.5 inches per two months) and the last recorded data (39.5 inches). I then realized that there was six months until 36 weeks. Still keeping in mind that the rate of change was 1.5 per two months, I multiplied 1.5 by 6 and then divided by 2 (because it was every two months and not one). This came out to be that she would grow 4.5 inches in 6 months. I then added 4.5 to 39.5 (the length at 30 months) and got a total of 44 inches. This would mean that Grace would be 44 inches long at 36 weeks. This would make sense because the rate of change was used, and if one subtracted the rate of change by 0.7 for 6 months from 44, they would get an answer of 39.5.
Hope this helped:)
