Need with performance task in ! i will mark you brainliest and give you extra points! 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?

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:)

I hope this helps :D, pls mark brainliest

By The Way The Answers Are In Bold

Explain

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

I will use points (4, 20) and (8, 23) to find the rate of change for baby Grace. First I will put the points into slope-intercept form (23-20 / 8-4), which gives me ¾. This means that baby Grace grows three-fourths of an inch every month.

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

The equation for point-slope form is y – y1 = m (x – x1).  The point I will use is (12, 26). The slope of her growth is ¾. So, the equation will now be y – 26 = ¾ (x – 12). After applying the distributive property you get y – 26 = 3/4x – 9. Then you will simplify the equation to y = 3/4x + 17. This means that every month baby Grace grows ¾ of an inch, and when she was born her height was 17 inches.  

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)

In the equation (y = 3/4x + 17), b is equal to the starting height of baby Grace, while x is the number of months. I can check this by applying the equation into a point (4, 20). First, you would substitute the x and y coordinates (4, 20), into the x and y values inside the equation. That will give me y = ¾(4) + 17. After simplifying you will get 20 = 3 + 17, which is true. So this ensures that  baby Grace was born 17 inches tall.

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.

When baby Grace is 36 months old she will be about 44 inches tall. If you apply the x value into the equation y = 3/4x + 17, you will get y = ¾(36) + 17. After applying the distributive property you get y = 27 + 17. After adding these 2 numbers the final answer is y = 44. My answer makes sense because if you apply the x value into the equation you will get the same results.

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