Section 6.2 - Lines Of Best Fit

1.

The table shows the Olympic gold medal performance in high jump from 1948-1980. Which shows a line of best fit for the data?

Graph a

Graph b

Graph c

Graph d

Graph a shows a line of best fit for the data because it represents a clear upward trend in the performance of Olympic gold medalists in high jump from 1948-1980. The line in graph a has a positive slope, indicating an increase in performance over time. The other graphs do not show a clear trend or have a negative slope, which does not accurately represent the data.

Explanation

Graph a shows a line of best fit for the data because it represents a clear upward trend in the performance of Olympic gold medalists in high jump from 1948-1980. The line in graph a has a positive slope, indicating an increase in performance over time. The other graphs do not show a clear trend or have a negative slope, which does not accurately represent the data.

2.

The following data show the video game rankings of two students, from least favorite (1) to most favorite (10). Which is the equation for the line of best fit?

Y = -0.75x + 9.75

Y = 0.75x + 8.25

Y = 0.75x + 9.75

Y = -0.75x + 8.25

The equation for the line of best fit represents the relationship between the video game rankings of the two students. The equation y = -0.75x + 9.75 indicates that as the video game ranking (x) increases, the overall favorability rating (y) decreases at a rate of 0.75. The y-intercept of 9.75 suggests that when the video game ranking is 0, the favorability rating is 9.75. This equation best fits the given data and represents the trend observed in the rankings.

Explanation

The equation for the line of best fit represents the relationship between the video game rankings of the two students. The equation y = -0.75x + 9.75 indicates that as the video game ranking (x) increases, the overall favorability rating (y) decreases at a rate of 0.75. The y-intercept of 9.75 suggests that when the video game ranking is 0, the favorability rating is 9.75. This equation best fits the given data and represents the trend observed in the rankings.

3.

The table and scatter plot show the mean heights of children in Kalama, Egypt, a village where nutrition is being studied. What is an equation for the line of best fit?

Y = 0.15x + 74.15

Y = 0.65x + 64.65

Y = -0.65x + 89.35

Y = 0.65x - 31.05

The equation for the line of best fit, y = 0.65x + 64.65, suggests that there is a positive linear relationship between the height of children in Kalama, Egypt and the variable x. The slope of 0.65 indicates that for every unit increase in x, the height of the children is expected to increase by 0.65 units. The y-intercept of 64.65 suggests that when x is 0, the predicted height of the children is 64.65. This equation represents the trend observed in the data and can be used to make predictions about the height of children based on their nutrition.

Explanation

The equation for the line of best fit, y = 0.65x + 64.65, suggests that there is a positive linear relationship between the height of children in Kalama, Egypt and the variable x. The slope of 0.65 indicates that for every unit increase in x, the height of the children is expected to increase by 0.65 units. The y-intercept of 64.65 suggests that when x is 0, the predicted height of the children is 64.65. This equation represents the trend observed in the data and can be used to make predictions about the height of children based on their nutrition.

4.

This scatter plot shows daily low temperature s in Banff National Park for the first ten days of July. What is the equation for the line of best fit?

Y = x + 4

Y = 7/3x + 2/3

Y = 7/3x + 16/3

Y = x + 2

The equation for the line of best fit in this scatter plot represents the relationship between the daily low temperatures and the days in July. The equation y = x + 2 suggests that for each day in July, the corresponding low temperature is equal to the day number plus 2. This indicates that the low temperatures are increasing gradually as the days progress in July.

Explanation

The equation for the line of best fit in this scatter plot represents the relationship between the daily low temperatures and the days in July. The equation y = x + 2 suggests that for each day in July, the corresponding low temperature is equal to the day number plus 2. This indicates that the low temperatures are increasing gradually as the days progress in July.

5.

The data shows the price and manufacturing time for various bowls. Write the equation you could use to determine the price for a bowl that takes 45 minutes to manufacture.

45 = 2.7x - 4.8b

Y = 2.7x - 4.8(45)

Y = 2.7(45) - 4.8b

45y = 2.7x - 4.8b

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Explanation

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6.

This scatter plot shows the annual profits for the past ten years for Ellen's business designing greeting cards. Use the graph to estimate the profit in the 9th year.

$12 500

$13 200

$13 500

$14 000

Based on the scatter plot, we can see that the profit values for each year are increasing gradually. In the 9th year, the profit value seems to be slightly above the midpoint between $13,000 and $13,500. Therefore, we can estimate the profit in the 9th year to be around $13,200.

Explanation

Based on the scatter plot, we can see that the profit values for each year are increasing gradually. In the 9th year, the profit value seems to be slightly above the midpoint between $13,000 and $13,500. Therefore, we can estimate the profit in the 9th year to be around $13,200.

7.

This scatter plot shows average ticket sales for different summer temperatures. Use the graph to estimate the number of tickets sold on a day when it is 35C

465

490

540

600

Based on the scatter plot, there is a negative correlation between temperature and ticket sales. As the temperature increases, the number of tickets sold decreases. Therefore, on a day when it is 35C, we can estimate that the number of tickets sold would be around 465, which is the closest value on the scatter plot to 35C.

Explanation

Based on the scatter plot, there is a negative correlation between temperature and ticket sales. As the temperature increases, the number of tickets sold decreases. Therefore, on a day when it is 35C, we can estimate that the number of tickets sold would be around 465, which is the closest value on the scatter plot to 35C.

8.

The scatter plot shows the fuel consumption for vehicles of various weights. Use the graph to estimate the weight of a car that consumes fuel at a rate of 5L / 100km.

1.0 tonne

1.06 tonnes

1.1 tonnes

1.6 tonnes

Based on the scatter plot, we can see that as the weight of the vehicles increases, the fuel consumption also tends to increase. The estimated weight of a car that consumes fuel at a rate of 5L / 100km falls between 1.0 tonne and 1.1 tonnes on the graph. The closest option is 1.06 tonnes, which is the most reasonable estimate based on the trend shown in the scatter plot.

Explanation

Based on the scatter plot, we can see that as the weight of the vehicles increases, the fuel consumption also tends to increase. The estimated weight of a car that consumes fuel at a rate of 5L / 100km falls between 1.0 tonne and 1.1 tonnes on the graph. The closest option is 1.06 tonnes, which is the most reasonable estimate based on the trend shown in the scatter plot.

9.

Ananya is member of the school swim team. The average number of laps she swims during practice for various times is shown below. Use a line of best fit to estimate how long it will take Ananya to swim 100 laps.

52 min

55 min

59 min

160 min

Based on the given information, Ananya's average time to swim a certain number of laps is increasing gradually. Since there is no information about her time for 100 laps specifically, we can estimate it by drawing a line of best fit through the given data points. By extending this line to the point where Ananya swims 100 laps, we can estimate that it will take her approximately 55 minutes.

Explanation

Based on the given information, Ananya's average time to swim a certain number of laps is increasing gradually. Since there is no information about her time for 100 laps specifically, we can estimate it by drawing a line of best fit through the given data points. By extending this line to the point where Ananya swims 100 laps, we can estimate that it will take her approximately 55 minutes.

10.

The following data shows the price per carat for various weights of loose diamonds. Which two points could you use to determine the equation for the line of best fit?

(0.3, 1779) and (43, 33 101)

(0.5, 2813) and (3, 14 021)

(2, 12 823) and (3, 14 021)

(0.9, 4929) and (2, 12 823)

The two points (0.9, 4929) and (2, 12 823) can be used to determine the equation for the line of best fit because they represent different weights of diamonds and their corresponding prices per carat. By plotting these points on a graph and drawing a line of best fit, we can estimate the relationship between the weight of a diamond and its price per carat. These two points provide a good range of data to determine the slope and intercept of the line, which can be used to calculate the equation of the line of best fit.

Explanation

The two points (0.9, 4929) and (2, 12 823) can be used to determine the equation for the line of best fit because they represent different weights of diamonds and their corresponding prices per carat. By plotting these points on a graph and drawing a line of best fit, we can estimate the relationship between the weight of a diamond and its price per carat. These two points provide a good range of data to determine the slope and intercept of the line, which can be used to calculate the equation of the line of best fit.