Question

1. dangelo recorded his height on his door frame from when he was 9 years old until 13 years old. graph his age and height.

age (years)	9	10	11	12	13

graph with age (years) on x - axis and height (inches) on y - axis

1. describe dangelos height as he gets older.

1. using the graph from question 1, predict how tall dangelo will be when he turns 14 years old.

1. write the equation of a line that passes through the points (0,4) and (8,0).

1. write a rule that represents the function in the table.

x	y
4.5	0
3	- 1
0	- 3

1. determine the rate of change of the function in the table below.

x	0	1	2	3	4

Explanation:

Question 1: Graphing Age and Height

Step1: Identify Axes

Let the x - axis represent age (in years) and the y - axis represent height (in inches). The x - values are 9, 10, 11, 12, 13 and the corresponding y - values are 56, 57, 59, 60, 64.

Step2: Plot Points

For age = 9 (x = 9), height = 56 (y = 56), plot the point (9, 56). For age = 10 (x = 10), height = 57 (y = 57), plot (10, 57). For age = 11 (x = 11), height = 59 (y = 59), plot (11, 59). For age = 12 (x = 12), height = 60 (y = 60), plot (12, 60). For age = 13 (x = 13), height = 64 (y = 64), plot (13, 64).

Step3: Connect Points (Optional for Scatter Plot)

If we want to show the trend, we can connect the plotted points with line segments.

Question 2: Describe Height with Age

As D'Angelo's age increases from 9 to 13 years, his height generally increases. From 9 to 10, height increases by 1 inch (57 - 56 = 1), from 10 to 11 by 2 inches (59 - 57 = 2), from 11 to 12 by 1 inch (60 - 59 = 1), and from 12 to 13 by 4 inches (64 - 60 = 4). Overall, there is a positive trend in height as age increases.

Step1: Analyze Trend

Looking at the height changes: 56 (9), 57 (10) (change + 1), 59 (11) (change + 2), 60 (12) (change + 1), 64 (13) (change + 4). The average rate of change from 9 to 13: total change in height = 64 - 56 = 8, total change in age = 13 - 9 = 4, average rate = 8/4 = 2 inches per year.

Step2: Predict at 14

At 13, height is 64. If we assume a similar trend (using the average rate of 2 inches per year), at 14 (1 year after 13), height would be 64+2 = 66 inches (this is a rough prediction, the actual change could vary as the growth rate is not constant).

Question 4: Equation of Line through (0,4) and (8,0)

Answer:

D'Angelo's height generally increases as he gets older (from 9 to 13 years).

Question 3: Predict Height at 14