SOLUTION: Find the standard form of the equation of the line that passes through the points (6,-2) and (14,8). thanks

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Question 668989: Find the standard form of the equation of the line that passes through the points (6,-2) and (14,8).
thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=6 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=14 and y%5B2%5D=8.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%288--2%29%2F%2814-6%29 Plug in y%5B2%5D=8, y%5B1%5D=-2, x%5B2%5D=14, and x%5B1%5D=6


m=%2810%29%2F%2814-6%29 Subtract -2 from 8 to get 10


m=%2810%29%2F%288%29 Subtract 6 from 14 to get 8


m=5%2F4 Reduce


So the slope of the line that goes through the points and is m=5%2F4


Now let's use the point slope formula:


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


y--2=%285%2F4%29%28x-6%29 Plug in m=5%2F4, x%5B1%5D=6, and y%5B1%5D=-2


y%2B2=%285%2F4%29%28x-6%29 Rewrite y--2 as y%2B2


4%28y%2B2%29=5%28x-6%29 Multiply both sides by 4


4y%2B8=5x-30 Distribute


4y=5x-30-8 Subtract 8 from both sides.


4y-5x=-30-8 Subtract 5x from both sides.


-5x%2B4y=-38 Combine like terms.


5x-4y=38 Multiply everything by -1 to make the x coefficient positive


So the answer is 5x-4y=38