Please Help!!!! 100 points!!!
Baby Grace Graph -
a) Use the data in the table to find the rate of change in the length of baby girl Grace.
b) Write a linear equation for the graph in point-slope form. Show your work.
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.
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.

Baby Claire Graph -
a) Determine the slope of the line. Show your work.
b) Is baby girl Claire growing at a faster rate than baby girl Grace? Justify your answer.
c) Use point-slope form to write a linear equation to represent the growth of Claire overtime. Then, simplify the equation and write it in slope-intercept form. Identify the y-intercept. Show your work.
d) Based on the data, how long was Claire at birth? Explain.

Baby Grace's rate of change is 0.75 inches per month
Her equation is: [tex]y - 20= 0.75(x - 4)[/tex].
Her length at birth was 17 inches, while her length in 36 months will be 44 inches
Baby Clair's slope is 2 inches per month
Baby Clair has a faster growing rate
Her equation is [tex]y - 22 = 2(x - 4)[/tex].
Her length at birth was 14 inches

Baby Grace

(a) The rate of change

Select any two points from the given table

[tex](x_1,y_1)=(4,20)[/tex]

[tex](x_2,y_2)=(8,23)[/tex]

The rate of change (m) is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{23 - 20}{8 - 4}[/tex]

[tex]m = \frac{3}{4}[/tex]

[tex]m=0.75[/tex]

The rate of change is 0.75 inches per month

(b) The linear equation

The equation in point slope form is:

[tex]y - y_1 = m(x - x_1)[/tex]

So, we have:

[tex]y - 20= 0.75(x - 4)[/tex]

(c) Her length at birth

At birth, the number of months is 0

i.e. x = 0

So, we have:

[tex]y - 20= 0.75(0 - 4)[/tex]

[tex]y - 20= 0.75(- 4)[/tex]

[tex]y - 20= -3[/tex]

Solve for y

[tex]y = 20 - 3[/tex]

[tex]y = 17[/tex]

Her length at birth was 17 inches

(d) Her length in 36 months time

This means that: x = 36

So, we have:

[tex]y - 20= 0.75(36 - 4)[/tex]

[tex]y - 20= 0.75(32)[/tex]

[tex]y - 20= 24[/tex]

Solve for y

[tex]y = 20+ 24[/tex]

[tex]y = 44[/tex]

Her length in 36 months will be 44 inches

Baby Claire

(a) The slope

Select any two points from the given graph

[tex](x_1,y_1)=(4,22)[/tex]

[tex](x_2,y_2)=(14,30)[/tex]

The rate of change (m) is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{30 - 22}{14 - 4}[/tex]

[tex]m = \frac{8}{4}[/tex]

[tex]m = 2[/tex]

The slope is 2 inches per month

(b) Compare their growing rates

Baby Grace growing rate is 0.75 inches per month

Baby Clair growing rate is 2 inches per month

By comparison,

Baby Clair has a faster growing rate

(c) The linear equation

The equation in point slope form is:

[tex]y - y_1 = m(x - x_1)[/tex]

So, we have:

[tex]y - 22 = 2(x - 4)[/tex]

(d) Her length at birth

This means that: x = 0

So, we have:

[tex]y - 22 = 2(x - 4)[/tex]

[tex]y - 22 = 2(0 - 4)[/tex]

[tex]y - 22 = 2(- 4)[/tex]

[tex]y - 22 = - 8[/tex]

Solve for y

[tex]y = 22- 8[/tex]

[tex]y =14[/tex]

Her length at birth was 14 inches

Read more about linear equations at:

https://brainly.com/question/11897796