SOLUTION: find the equation of each line: the line is parallel to -3x+2y=9 and contains the point (-2,1).

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Question 168840: find the equation of each line:
the line is parallel to -3x+2y=9 and contains the point (-2,1).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-3x%2B2y=9 Start with the given equation.


2y=9%2B3x Add 3x to both sides.


2y=3x%2B9 Rearrange the terms.


y=%283x%2B9%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%283%2F2%29x%2B9%2F2 Break up the fraction.



We can see that the equation y=%283%2F2%29x%2B9%2F2 has a slope m=3%2F2 and a y-intercept b=9%2F2.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=3%2F2.


Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=3%2F2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-1=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=1


y-1=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-1=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute


y-1=%283%2F2%29x%2B3 Multiply


y=%283%2F2%29x%2B3%2B1 Add 1 to both sides.


y=%283%2F2%29x%2B4 Combine like terms.


So the equation of the line parallel to -3x%2B2y=9 that goes through the point is y=%283%2F2%29x%2B4.


Here's a graph to visually verify our answer:
Graph of the original equation y=%283%2F2%29x%2B9%2F2 (red) and the parallel line y=%283%2F2%29x%2B4 (green) through the point .