For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following line:
![2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4](https://tex.z-dn.net/?f=2x-3y%20%3D%2012%5C%5C2x-12%20%3D%203y%5C%5Cy%20%3D%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x-4)
If the line we wish to find is perpendicular to the one given, then its slope is given by:
![m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}](https://tex.z-dn.net/?f=m_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-1%7D%20%7Bm_%20%7B1%7D%7D%5C%5Cm_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-1%7D%20%7B%5Cfrac%20%7B2%7D%20%7B3%7D%7D%5C%5Cm_%20%7B2%7D%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B2%7D)
Then the line is:
![y = - \frac {3} {2} x + b](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B2%7D%20x%20%2B%20b)
We substitute the point:
![6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9](https://tex.z-dn.net/?f=6%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B2%7D%20%282%29%20%2B%20b%5C%5C6%20%3D%20-3%20%2B%20b%5C%5Cb%20%3D%206%20%2B%203%5C%5Cb%20%3D%209)
Finally, the equation is:
![y = - \frac {3} {2} x + 9](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B2%7D%20x%20%2B%209)
Answer:
![y = - \frac {3} {2} x + 9](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B3%7D%20%7B2%7D%20x%20%2B%209)
Answer:
Step-by-step explanation:
1.153846153846
<h2>Answer:</h2><h3>E.30</h3>
Correct me if wrong :)