Questions: A scatter plot is shown below. A line of best fit passes through point A and another point in the data set. Use the drop-down menus to describe through which additional point the line of best fit passes and use that line to determine the approximate value for y when x=9.

A scatter plot is shown below. A line of best fit passes through point A and another point in the data set. Use the drop-down menus to describe through which additional point the line of best fit passes and use that line to determine the approximate value for y when x=9.
Transcript text: A scatter plot is shown below. A line of best fit passes through point $A$ and another point in the data set. Use the drop-down menus to describe through which additional point the line of best fit passes and use that line to determine the approximate value for $y$ when $x=9$.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify Point A

Point A is located at (2, 3).

Step 2: Find another point for the line of best fit

A line of best fit should pass through the middle of the data points, minimizing the distance to the points on either side. Visually, a line through A and B (10, 8.5) seems like a good fit. Another possible point could be C (6,5), but this line does not fit as well since more points will be farther away.

Step 3: Calculate the slope

Using points A (2, 3) and B (10, 8.5), the slope is (8.5 - 3) / (10 - 2) = 5.5 / 8 = 0.6875.

Step 4: Find the equation of the line

Using point-slope form with point A (2,3): y - 3 = 0.6875(x - 2). Simplifying to slope-intercept form gives y = 0.6875x + 1.625

Step 5: Approximate y when x = 9

Substitute x = 9 into the equation: y = 0.6875 * 9 + 1.625 = 6.1875 + 1.625 = 7.8125. Since the graph uses whole numbers, round to approximately 8.

Final Answer

The line of best fit passes through point B. When x = 9, y is approximately 8.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Change each equation to its equivalent logarithmic form. (a) 9^(4z) = 4 (b) e^z = 6 (c) c^Z = f (a) Find the equivalent equation for 9^(4z) = 4.
failedAnswered
What distinguished the New Left from the "Old Left"? The New Left used violent revolutionary cells like the Weather Underground to force revolutionary change on a skeptical American public, while the Old Left was content to use traditional institutions like the Socialist party. The Old Left was primarily concerned with improving the conditions of the working class through voluntary societies, while the New Left sought to inspire college students to grassroots social activism. The Old Left was strictly focused on inspiring class resentment and violent revolutionary anger among workers toward the bourgeoisie, while the New Left sought to gradually take control of the federal government and impose socialism on American society from the top down. The New Left sought to use grassroots democracy and nonviolent demonstrations to give power to the people and change society, while the Old Left focused on orthodox Marxism. The New Left ideology spread to many other aspects of society and came to influence elite culture, while the Old Left remained an ideology of the working class and exerted little influence.
failedAnswered
Evaluate the function f(r)=sqrt(r+3)+9 at the given values of the independent variable and simplify. a. f(-3) b. f(61) c. f(x-3)
failedAnswered
Chapter 10 - Problem Assignment Diaz Company owns a machine that cost 126,200 and has accumulated depreciation of 93,400. Prepare the entry to record the disposal of the machine on January 1 in each separate situation. 1. The machine needed extensive repairs and was not worth repairing. Diaz disposed of the machine, receiving nothing in return. 2. Diaz sold the machine for 16,100 cash. 3. Diaz sold the machine for 32,800 cash. 4. Diaz sold the machine for 41,500 cash.
failedAnswered
m = 3 n = 5 M, D = ?, N