SOLUTION: (6,10),(4,1)

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Question 559807: (6,10),(4,1)
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=10.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=1.


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


m=%281-10%29%2F%284-6%29 Plug in y%5B2%5D=1, y%5B1%5D=10, x%5B2%5D=4, and x%5B1%5D=6


m=%28-9%29%2F%284-6%29 Subtract 10 from 1 to get -9


m=%28-9%29%2F%28-2%29 Subtract 6 from 4 to get -2


m=9%2F2 Reduce


So the slope of the line that goes through the points and is m=9%2F2


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-10=%289%2F2%29%28x-6%29 Plug in m=9%2F2, x%5B1%5D=6, and y%5B1%5D=10


y-10=%289%2F2%29x%2B%289%2F2%29%28-6%29 Distribute


y-10=%289%2F2%29x-27 Multiply


y=%289%2F2%29x-27%2B10 Add 10 to both sides.


y=%289%2F2%29x-17 Combine like terms.


y=%289%2F2%29x-17 Simplify


So the equation that goes through the points and is y=%289%2F2%29x-17


Notice how the graph of y=%289%2F2%29x-17 goes through the points and . So this visually verifies our answer.
Graph of y=%289%2F2%29x-17 through the points and
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