payton collected data to show the relationship between the number of hours he practices and the number of…

payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. the table shows his data. practice makes better number of hours 1 2 3 4 5 6 7 8 number of errors 36 34 30 31 23 16 11 5 which is the approximate slope of the line of best fit for the data? -5.5 -4.5 -2.0 -1.0

payton collected data to show the relationship between the number of hours he practices and the number of errors he makes when playing a new piece of music. the table shows his data. practice makes better number of hours 1 2 3 4 5 6 7 8 number of errors 36 34 30 31 23 16 11 5 which is the approximate slope of the line of best fit for the data? -5.5 -4.5 -2.0 -1.0

Answer

Explanation:

Step1: Recall slope formula

The formula for the slope $m$ of the line of best - fit using two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can also use a more general method for multiple data points. A quick way is to take two points that seem to represent the trend well. Let's take the first point $(1,36)$ and the last point $(8,5)$.

Step2: Substitute values into formula

Here $x_1 = 1,y_1=36,x_2 = 8,y_2 = 5$. Then $m=\frac{5 - 36}{8 - 1}=\frac{- 31}{7}\approx - 4.43\approx - 4.5$.

Answer:

-4.5