SOLUTION: How do I write the equation of a line that is parallel to 3x-2y=8 and contains the point (-1,4) ?

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Question 236694: How do I write the equation of a line that is parallel to 3x-2y=8 and contains the point (-1,4) ?
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

3x-2y=8 Start with the given equation.


-2y=8-3x Subtract 3x from both sides.


-2y=-3x%2B8 Rearrange the terms.


y=%28-3x%2B8%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%28%28-3%29%2F%28-2%29%29x%2B%288%29%2F%28-2%29 Break up the fraction.


y=%283%2F2%29x-4 Reduce.


We can see that the equation y=%283%2F2%29x-4 has a slope m=3%2F2 and a y-intercept b=-4.


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-4=%283%2F2%29%28x--1%29 Plug in m=3%2F2, x%5B1%5D=-1, and y%5B1%5D=4


y-4=%283%2F2%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-4=%283%2F2%29x%2B%283%2F2%29%281%29 Distribute


y-4=%283%2F2%29x%2B3%2F2 Multiply


y=%283%2F2%29x%2B3%2F2%2B4 Add 4 to both sides.


y=%283%2F2%29x%2B11%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line parallel to 3x-2y=8 that goes through the point is y=%283%2F2%29x%2B11%2F2.


Here's a graph to visually verify our answer:
drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%283%2F2%29x-4%2C%283%2F2%29x%2B11%2F2%29%2C%0D%0Acircle%28-1%2C4%2C0.08%29%2C%0D%0Acircle%28-1%2C4%2C0.10%29%2C%0D%0Acircle%28-1%2C4%2C0.12%29%29

Graph of the original equation y=%283%2F2%29x-4 (red) and the parallel line y=%283%2F2%29x%2B11%2F2 (green) through the point .