The generic equation of the line is:

Where,
m: slope of the line.
b: cutting point with vertical axis.
The slope of the line is given by:



The cutting point with the vertical axis is:

Therefore, the equation of the line is:

Answer:
the equation that represents Emily’s situation is:

Answer:
The answer is
![\bold{ \left[\begin{array}{c}\frac{127}{27} \\ \ &\frac{65}{18} \\ \ &\frac{76}{27}\\ \ &\frac{97}{54}\\\ \end{array}\right]}](https://tex.z-dn.net/?f=%5Cbold%7B%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B127%7D%7B27%7D%20%5C%5C%20%5C%20%26%5Cfrac%7B65%7D%7B18%7D%20%5C%5C%20%5C%20%26%5Cfrac%7B76%7D%7B27%7D%5C%5C%20%5C%20%26%5Cfrac%7B97%7D%7B54%7D%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%7D)
Step-by-step explanation:
Given value:
The value of
:
![= \left[\begin{array}{c}5&4&3&2\\ \end{array}\right] \left[\begin{array}{c}-4&5&-2&3\\ \end{array}\right]](https://tex.z-dn.net/?f=%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D5%264%263%262%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%20%5Cend%7Barray%7D%5Cright%5D)
The above value "
" are orthogonal vectors that is: 
from the above orthogonal basis of subspace w and the shortest distanc value of vector y:
![=\left[\begin{array}{c}3&9&-5&8\\\ \end{array}\right] \\\\](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%269%26-5%268%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C)
The value of y on 
![\frac{\left[\begin{array}{c}3&9&5&-8\\\ \end{array}\right] \cdot \left[\begin{array}{c}-4&5&-2&3\\ \end{array}\right] }{\left[\begin{array}{c}-4&5&-2&3\\ \end{array}\right] \cdot \left[\begin{array}{c}-4&5&-2&3\\ \end{array}\right]} \times \left[\begin{array}{c}-4&5&-2&3\\ \end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%269%265%26-8%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%7D%20%5Ctimes%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%20%5Cend%7Barray%7D%5Cright%5D)
![= \frac{50}{54} \left[\begin{array}{c}5&4&3&2\\\ \end{array}\right] - \frac{1}{54} \left[\begin{array}{c}-4&5&-2&3\\\ \end{array}\right]\\\\](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B50%7D%7B54%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D5%264%263%262%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%20%20-%20%5Cfrac%7B1%7D%7B54%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%265%26-2%263%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C)
![= \left[\begin{array}{c}\frac{127}{27} \\ \ &\frac{65}{18} \\ \ &\frac{76}{27}\\ \ &\frac{97}{54}\\\ \end{array}\right]](https://tex.z-dn.net/?f=%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B127%7D%7B27%7D%20%5C%5C%20%5C%20%26%5Cfrac%7B65%7D%7B18%7D%20%5C%5C%20%5C%20%26%5Cfrac%7B76%7D%7B27%7D%5C%5C%20%5C%20%26%5Cfrac%7B97%7D%7B54%7D%5C%5C%5C%20%5Cend%7Barray%7D%5Cright%5D)
Answer:
Her equation system is incorrect
Step-by-step explanation:
Remember that
1 dime=$0.10
1 quarter=$0.25
Let
x------> the number of quarters
y-----> the number of dimes
we know that
0.25x+0.10y=20.70 ------> equation A
x=10+y -----> equation B
Her equation system is incorrect, because in her second equation she exchanged the variables, using x instead of y and y instead of x.
Snallest to the greatest
0.6, 0.7, 0.83