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	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

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 use two - point method to approximate the slope of the line of best - fit. Let's take the first point \((x_1,y_1)=(1,36)\) and the last point \((x_2,y_2)=(8,5)\).

Step2: Substitute values into formula

Substitute \(x_1 = 1,y_1 = 36,x_2 = 8,y_2 = 5\) into the slope formula:
\[m=\frac{5 - 36}{8 - 1}=\frac{- 31}{7}\approx - 4.43\approx - 4.5\]

Answer:

-4.5