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\n| number of hours | number of errors |\n| ---- | ---- |\n| 1 | 36 |\n| 2 | 34 |\n| 3 | 30 |\n| 4 | 31 |\n| 5 | 23 |\n| 6 | 16 |\n| 7 | 11 |\n| 8 | 5 |\nwhich is the approximate slope of the line of best fit for the data?\n-5.5\n-4.5\n-2.0\n-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\n| number of hours | number of errors |\n| ---- | ---- |\n| 1 | 36 |\n| 2 | 34 |\n| 3 | 30 |\n| 4 | 31 |\n| 5 | 23 |\n| 6 | 16 |\n| 7 | 11 |\n| 8 | 5 |\nwhich is the approximate slope of the line of best fit for the data?\n-5.5\n-4.5\n-2.0\n-1.0

Answer

Explanation:

Step1: Recall slope formula

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can take two - points from the table. Let's take $(x_1,y_1)=(1,36)$ and $(x_2,y_2)=(2,34)$.

Step2: Substitute values into formula

$m=\frac{34 - 36}{2 - 1}=\frac{-2}{1}=- 2$. We can also check with other pairs. Let's take $(x_1,y_1)=(3,30)$ and $(x_2,y_2)=(4,31)$. $m=\frac{31 - 30}{4 - 3}=1$. But if we take more pairs and use a more accurate method (least - squares regression which is beyond basic arithmetic for a quick estimate), we can see that as the number of hours $x$ increases, the number of errors $y$ generally decreases. Averaging out the changes between pairs, we find that the slope is approximately $-4.5$. For example, from $(1,36)$ to $(8,5)$: $m=\frac{5 - 36}{8 - 1}=\frac{-31}{7}\approx - 4.43\approx - 4.5$.

Answer:

-4.5