So for 4, first thing you need is slope. Choose 2 points. I am choosing (8,2) and (6,3) So, then its the second y term subtracted by the first y term over(Or divided by) the second x term subtracted by the first x term.
3-2/6-8 or 1/-2 or -.5 (negative 0.5)
Now, time to find the yintercept(yint). So, choose one of the points, Im choosing (8,2), and put it into slope intercept, but leave yint as b.
(2)=-.5(8)+b
simplify
2= -4+b
subtract -4
b=6
So, your answer is y= -0.5x+6
I will right number 6 in anoher answer
Hey!
To find out how much it is in cups, we must know how many cups 1 quart is equal to.
1 quart = 4 cups.
5 1/2 (or 5.5) quarts = 22 cups.
The question is missing. Here is the complete question.
Let y = ![\left[\begin{array}{ccc}2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
and u = ![\left[\begin{array}{ccc}7\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.
Answer: y = ![\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%20%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B-1%7D%7B10%7D%5C%5C%20%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation: The sum of vectors is given by
y = 
+ z
where is in Span(u);
vector z is orthogonal to it;
First you have to compute the orthogonal projection of y:
= proj y = 
Calculating orthogonal projection:
![\left[\begin{array}{c}2\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
.![\left[\begin{array}{c}7\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{c}9\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
. = ![\left[\begin{array}{c}49\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D49%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Calculating vector z:
z = y -
z = ![\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
z = ![\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Writing y as the sum:
![y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
The answer is 6.561×10^−7, I put the steps in the picture. Hope this helps, have a blessed day! :-)
