SOLUTION: what is the slope intercept equation of the line passing through the points (1,7) and (3,3)

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Question 537672: what is the slope intercept equation of the line passing through the points (1,7) and (3,3)
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=1 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=3.


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


m=%283-7%29%2F%283-1%29 Plug in y%5B2%5D=3, y%5B1%5D=7, x%5B2%5D=3, and x%5B1%5D=1


m=%28-4%29%2F%283-1%29 Subtract 7 from 3 to get -4


m=%28-4%29%2F%282%29 Subtract 1 from 3 to get 2


m=-2 Reduce


So the slope of the line that goes through the points and is m=-2


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-7=-2%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=7


y-7=-2x%2B-2%28-1%29 Distribute


y-7=-2x%2B2 Multiply


y=-2x%2B2%2B7 Add 7 to both sides.


y=-2x%2B9 Combine like terms.


So the equation that goes through the points and is y=-2x%2B9


Notice how the graph of y=-2x%2B9 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B9 through the points and


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Jim