Pediatricians will measure and track the growth of an infant’s weight and length to be sure the baby is thriving and growing properly. The growth of baby girl Grace is displayed in the data table below.

Growth Chart for Baby Girl Grace
(4–30 Months)
Months 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Length (inches) 20 21.5 23 24.5 26 27.5 29 30.5 32 33.5 35 36.5 38 39.5

a) Use the data in the table to find the rate of change in the length of baby girl Grace. (2 points)

b) Write a linear equation for the graph in point-slope form. Show your work. (2 points)

c) Use your equation to determine how long Grace was at birth. Show your work and explain how you can check your result using your knowledge of rate of change. (3 points)

d) Based on the data, how long do you predict baby Grace will be at 36 months of age? Use the rate of change to justify your answer. Does your answer make sense? Explain. (2 points)

a) 0.75 inch/month

b) y-20 = 0.75(x-4)

c) 17 inches

d) 44

a) 0.8 inch/month

b) yes

c) y = 0.8x + 18.8

d) 18.8 inches

Step-by-step explanation:

a) (21.5-20)/(6-4) = 1.5/2

= 0.75 inch/month

If this is correct, 2 months after the 6th month (month 8), it should be

21.5 + 2(0.75) = 23

Which it is

b) y-y1 = m(x-x1)

Where y is the length, x is the months, m is the slope and (x1,y1) is a known point

At x = 4, y = 20

y-20 = 0.75(x-4)

Or

y = 0.75x + c

20 = 0.75(4) + c

c = 20 - 3 = 17

y = 0.75x + 17

c) at birth, 4 months before month 4

So, 20 - 0.75(4) = 17

Which is also the y-intercept

d) y = 0.75(36) + 17

y = 27 + 4 = 44 inches

Generally, at the age of 3 years (36 month) the length is between 35 and 40 inches

a) slope = (30-22)/(14-4)

= 0.8 inch/month

b) 0.8 > 0.75, so yes

c) When x = 4, y = 22

y-22 = 0.8(x - 4)

y - 22 = 0.8x - 3.2

y = 0.8x + 18.8

y-intercept is 18.8

d) at birth, x = 0.

Length was 18.8 inches

MARK BRAINLIEST

depending on others is critical to survival. my source is apex!

step-by-step explanation: