Question

use the data in the scatter plot to answer each question. drag the correct choice to each white box. the age and height of several trees at a tree farm are shown below. elves tree farm 1 if a tree is 4 years old, which is the best prediction of the height of the tree? 2 ft 4 ft 6 ft 2 if a tree is 10 feet tall, which is the best prediction of the age of the tree? 12 years 8 years 10 years 3 if a tree is 6 years old, which is not a reasonable prediction of the height of the tree? 5 ft 7 ft 9 ft

Explanation:

Question 1:

Step1: Analyze the scatter plot trend

The scatter plot shows a positive linear trend. For age = 4 years, check the trend line or cluster. At x = 4 (age), the height (y) on the trend or data points around x=4: the point at x=4 has y≈6? Wait, no, looking at the plot: when age is 4, the height (from the plot, the line or points: at x=4, the height is around 6 ft? Wait, the x-axis is age (years), y-axis height (ft). At x=4 (age 4), the data point or trend line: looking at the plot, the line passes near (4,6)? Wait, no, the first point at x=1 (age 1) is y=2, x=2 (age 2) y=3, x=4 (age 4) the point is at y=6? Wait, the plot: when age is 4, the height is 6 ft? Wait, the options are 2ft, 4ft, 6ft. So the best prediction is 6ft? Wait, no, wait the x-axis is age (years), so age 4: looking at the scatter plot, the point at age 4 (x=4) has y=6? Wait, the plot shows at x=4 (age 4), the height is 6 ft. So the best prediction is 6ft? Wait, no, maybe I misread. Wait, the first question: "If a tree is 4 years old, which is the best prediction of the height of the tree?" The options are 2ft, 4ft, 6ft. Looking at the scatter plot, at x=4 (age 4), the height (y) is around 6 ft? Wait, the plot: the x-axis is age (years), so age 4 is at x=4. The y-axis is height (ft). The data points: at x=1, y=2; x=2, y=3; x=4, the point is at y=6? Wait, the line drawn: from (1,2) to (8,10), slope is (10-2)/(8-1)=8/7≈1.14. So at x=4, y=2 + (8/7)*(3)≈2 + 3.43≈5.43, close to 6? So the best prediction is 6ft? Wait, no, the options are 2,4,6. So 6ft is the best.

Step2: Confirm with the plot

Looking at the scatter plot, at age 4 (x=4), the height is approximately 6 ft (the data point or trend line). So the best choice is 6ft.

Question 2:

Step1: Analyze the inverse relationship (height to age)

The scatter plot has age (x) and height (y). So for height = 10 ft (y=10), find x (age). From the plot, when y=10, x=8? Wait, no, the plot shows at y=10, x=8 (since at x=8, y=10). Wait, the options are 12 years, 8 years, 10 years. The trend line: when y=10, x=8. So the best prediction is 8 years.

Step2: Confirm with the plot

Looking at the scatter plot, the point at (8,10) is present. So when height is 10 ft, age is 8 years. So the best choice is 8 years.

Question 3:

Step1: Analyze age 6 (x=6) height predictions

For age 6 (x=6), the height (y) should be around the trend. The trend line: at x=6, y=2 + (8/7)*(5)≈2 + 5.71≈7.71. So reasonable heights are around 5-8 ft? Wait, the options are 5ft, 7ft, 9ft. 9ft is above the trend (at x=6, the data points are around 7-8 ft). So 9ft is not reasonable.

Step2: Confirm with the plot

At x=6 (age 6), the height data points are around 7-8 ft. 9ft is higher than the trend (since at x=8, height is 10, so at x=6, height should be less than 10, but the data points at x=6 are around 7-8). So 9ft is not a reasonable prediction.

Answer:

s:

1. 6 ft
2. 8 years
3. 9 ft