Answer:
1. The equation would be y = -2x + 9
Step-by-step explanation:
To find the line parallel going through the given point, first note that parallel lines have the same slope. This means that in #1, we have a slope of -2 in the original line, therefore the parallel line will also have a slope of -2. Now we can use this and the given point to find the line using point-slope form.
y - y1 = m(x - x1)
y - 1 = -2(x - 4)
y - 1 = -2x + 8
y = -2x + 9
Using y=Mx+b, the answer is y=10x-4.
The answer would be 16=3x
The mean absolute deviation of the number of books is 1.84
<h3>How to determine the mean absolute deviation?</h3>
The dot plot of the number of books is in the attached figure.
From the figure, we have:
x f
1 1
2 2
3 2
4 3
5 1
6 2
7 3
8 1
Start by calculating the mean using:
![\bar x= \frac{\sum fx}{\sum f}](https://tex.z-dn.net/?f=%5Cbar%20x%3D%20%5Cfrac%7B%5Csum%20fx%7D%7B%5Csum%20f%7D)
So, we have:
![\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}](https://tex.z-dn.net/?f=%5Cbar%20x%3D%20%5Cfrac%7B1%20%2A%201%20%2B%202%20%2A%202%20%2B%202%20%2A%203%20%2B%203%20%2A%204%20%2B%201%20%2A%205%20%2B%202%20%2A%206%20%2B%203%20%2A7%20%2B%201%20%2A%208%7D%7B1%20%2B2%2B2%2B3%2B1%2B2%2B3%2B1%7D)
Evaluate the sum and products
![\bar x= \frac{69}{15}](https://tex.z-dn.net/?f=%5Cbar%20x%3D%20%5Cfrac%7B69%7D%7B15%7D)
Divide
![\bar x= 4.6](https://tex.z-dn.net/?f=%5Cbar%20x%3D%204.6)
The mean absolute deviation is then calculated as:
![|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}](https://tex.z-dn.net/?f=%7C%5Cbar%20x%7C%20%3D%20%5Cfrac%7B%5Csum%20f%7Cx%20-%20%5Cbar%20x%7C%7D%7B%5Csum%20f%7D)
So, we have:
![|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}](https://tex.z-dn.net/?f=%7C%5Cbar%20x%7C%3D%20%5Cfrac%7B1%20%2A%20%7C1%20-4.6%7C%2B%202%20%2A%20%7C2%20-4.6%7C%20%2B%202%20%2A%20%7C3%20-4.6%7C%2B%203%20%2A%20%7C4%20-4.6%7C%2B%201%20%2A%7C%205%20-4.6%7C%2B%202%20%2A%20%7C6%20-4.6%7C%2B%203%20%2A%7C7%20-4.6%7C%2B%201%20%2A%20%7C8-4.6%7C%7D%7B1%20%2B2%2B2%2B3%2B1%2B2%2B3%2B1%7D)
Evaluate the absolute difference
![|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}](https://tex.z-dn.net/?f=%7C%5Cbar%20x%7C%3D%20%5Cfrac%7B1%20%2A%203.6%2B%202%20%2A%202.6%20%2B%202%20%2A%201.6%2B%203%20%2A%200.6%2B%201%20%2A0.4%2B%202%20%2A%201.4%2B%203%20%2A2.4%2B%201%20%2A%203.4%7D%7B15%7D)
Evaluate the sum of products
![|\bar x|= \frac{27.6}{15}](https://tex.z-dn.net/?f=%7C%5Cbar%20x%7C%3D%20%5Cfrac%7B27.6%7D%7B15%7D)
Divide
![|\bar x|= 1.84](https://tex.z-dn.net/?f=%7C%5Cbar%20x%7C%3D%201.84)
Hence, the mean absolute deviation of the number of books is 1.84
Read more about mean absolute deviation at:
brainly.com/question/3250070
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Answer:
y = 5/7 x -5
Step-by-step explanation:
X/7- y/5=1
Multiply each side by 35 to clear the fractions
35(X/7- y/5) =1*35
5x - 7y = 35
Subtract 5x from each side
5x-5x-7y = -5x+35
-7y = -5x+35
Divide each side by -7
-7y/-7 = -5x/-7 +35/-7
y = 5/7 x -5