SOLUTION: What is the slope intercept equation of the line that contains the points (5, 17) and (9, 13

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Question 205953: What is the slope intercept equation of the line that contains the points (5, 17) and (9, 13
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=5 and y%5B1%5D=17.
Also, is the second point . So this means that x%5B2%5D=9 and y%5B2%5D=13.


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


m=%2813-17%29%2F%289-5%29 Plug in y%5B2%5D=13, y%5B1%5D=17, x%5B2%5D=9, and x%5B1%5D=5


m=%28-4%29%2F%289-5%29 Subtract 17 from 13 to get -4


m=%28-4%29%2F%284%29 Subtract 5 from 9 to get 4


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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-17=-1%28x-5%29 Plug in m=-1, x%5B1%5D=5, and y%5B1%5D=17


y-17=-1x%2B-1%28-5%29 Distribute


y-17=-1x%2B5 Multiply


y=-1x%2B5%2B17 Add 17 to both sides.


y=-1x%2B22 Combine like terms.


y=-x%2B22 Simplify


So the equation that goes through the points and is y=-x%2B22