Answer:
<h2>The answer is option A</h2>
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
From the question the original line is
y = 2/3x - 7
Comparing with the general equation above
Slope = 2/3
Since the lines are parallel their slope are also the same
Slope of parallel line = 2/3
So the equation of the line using point
(12 , 2 ) and slope 2/3 is
![y - 2 = \frac{2}{3} (x - 12) \\ y - 2 = \frac{2}{3} x - 8 \\ y = \frac{2}{3} x - 8 + 2](https://tex.z-dn.net/?f=y%20-%202%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%28x%20-%2012%29%20%5C%5C%20y%20-%202%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20x%20-%208%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20x%20-%208%20%2B%202)
We have the final answer as
![y = \frac{2}{3} x - 6 \\](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20x%20-%206%20%5C%5C%20)
Hope this helps you