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The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?

The Motion Of An Object Was Recorded By Measuring The Velocity Of The Object In Meters Per Second At Various Times As Shown In The Table The Scatterplot Below W class=

Sagot :

anuksha0456

The equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

In the question, we are asked to find the equation of the line of BEST FIT for the given scatter plot.

We let the time be the independent variable x, and velocity is the dependent variable y.

We find the line of best fit using the least square method.

First, we calculate the mean:

  • of time (x), μ(x) = (0 + 2.1 + 5.3 + 8.2 + 10.0 + 12.1)/6 = 6.283333,
  • of velocity (y), μ(y) = (6.1 + 12.2 + 17.4 + 26.4 + 28.1 + 32.8)/6 = 20.5.

Now, we find the slope of the line of best fit, using the formula:

m = {∑(x - μ(x))(y - μ(y))}/{∑(x - μ(x))²}.

Taking value from the tables, which is attached, we get:

m = 239.35/109.2683333 = 2.190479096.

Now, we calculate the y-intercept of the line of best fit, using the formula:

b = μ(y) - m.μ(x),

or, b = 20.5 - 2.190479096*6.283333 = 6.736489681.

Now, the equation of the line of best fit, in the form of y = mx + b, can be written as, y = 2.190479096x + 6.736489681, which on approximation, and making y as v, the velocity, and x as t, the time, we get: v = 2.19t + 6.7.

Thus, the equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

Learn more about the least square method at

https://brainly.com/question/15088393

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