Step 1: Rate of change, slope, and writing linear functions 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)

(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

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

y-y1 = m(x-x1)

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)

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)

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

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)

Step 2: Comparing linear functions

The growth of baby girl Claire is displayed in the graph below.

a) Determine the slope of the line. Show your work. (2 points)

b) Is baby girl Claire growing at a faster rate than baby girl Grace? Justify your answer. (2 points)

c) Use point-slope form to write a linear equation to represent the growth of Claire over time. Then, simplify the equation and write it in slope-intercept form. Identify the y-intercept. Show your work. (3 points)

d) Based on the data, how long was Claire at birth? Explain. (2 points)

Step 3: Applying linear functions

Grace and Claire’s parents are saving money now for their college education. Function 1 shows the growth of baby Grace’s college fund over time. Function 2 shows growth of baby Claire’s college fund over time.

a) If Grace and Claire’s parents each invested $7,600 into a college saving account when the girls were born, how much money will each girl have for college when she turns 18? Explain. (2 points)

b) Do the functions show a positive or negative correlation between time and the amount of money saved? Explain. (1 point)

Step 4: Identifying functions as linear or nonlinear

As infants grow from a toddler to a young adult, there may be times when they are ill and medication is needed. It is extremely important that medication be administered in the exact dose so the child receives the correct amount. Too little or too much medication could have serious side effects. A popular children’s fever medicine manufacturer recommends the following dosage information to parents and pediatricians.

Children’s Fever Medicine

(given every 4–6 hours, as needed)

Weight 24+ lbs 36+ lbs 48+ lbs 60+ lbs 72+ lbs

Dosage 5 mL 7.5 mL 10 mL 12.5 mL 15 mL

a) Evaluate the data and find the rate of change from one age group to the next. Explain how you found the rate of change. (2 points)

b) Is the relationship between weight and the amount of medicine linear? Explain. (2 points)

PLEASE I WILL GIVE BRAINLIEST.