Question
6. The graph shows the weights of dogs and the time it took the same dogs to complete an agility course in seconds Which shows the line of best fit for the data? A) Seconds B) Seconds C) Seconds D) Seconds
Answer
4.3
(192 Votes)
Harry
Master · Tutor for 5 years
Answer
To determine the line of best fit for the data, we need to use the two points provided to calculate the slope of the line and then use one of the points to find the y-intercept.Step 1: Calculate the slope of the line.The slope (m) is calculated using the formula:m = (change in y) / (change in x)Using the points (20, 20) and (65, 60):m = (60 - 20) / (65 - 20)m = 40 / 45m = 8/9Step 2: Use one of the points and the slope to find the y-intercept (b).We can use the point-slope form of the equation of a line, which is:y - y1 = m(x - x1)Using the point (20, 20):20 - 20 = (8/9)(20 - x1)Since the left side of the equation is 0, we need to find the value of x1 when y is 0 to find the y-intercept.0 = (8/9)(x1 - 20)To find x1, we can multiply both sides by 9/8 to isolate x1:0 = x1 - 20x1 = 20This means that the y-intercept is at the point (20, 0).Step 3: Write the equation of the line of best fit.Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form (y = mx + b):y = (8/9)x + 20However, the y-intercept we calculated does not make sense in the context of the problem, as it suggests that a dog weighing 20 pounds would take 0 seconds to complete the course, which is not possible. We need to use the slope and one of the given points to find the correct y-intercept.Let's use the point (20, 20) again:20 = (8/9)(20) + bTo find b, we solve for b:20 = 160/9 + b20 = 17.78 + bb = 20 - 17.78b = 2.22Now we have the correct y-intercept.Step 4: Write the final equation of the line of best fit.y = (8/9)x + 2.22Answer:The line of best fit for the data is y = (8/9)x + 2.22. None of the options A, B, C, or D provided in the question text directly match this equation, so we cannot select one of them as the correct answer without more information. However, the process above shows how to find the line of best fit given the details of the scatter plot.