Question

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	number of errors
2	34
3	30
4	31
5	23
6	16
7	11
8	5

which is the approximate slope of the line of best fit for the data?
-5.5
-4.5
-2.0
-1.0

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