SOLUTION: what is the equation of the line that passes through (9, -2) and (4,6)?

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Question 550603: what is the equation of the line that passes through (9, -2) and (4,6)?
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=9 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=6.


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


m=%286--2%29%2F%284-9%29 Plug in y%5B2%5D=6, y%5B1%5D=-2, x%5B2%5D=4, and x%5B1%5D=9


m=%288%29%2F%284-9%29 Subtract -2 from 6 to get 8


m=%288%29%2F%28-5%29 Subtract 9 from 4 to get -5


m=-8%2F5 Reduce


So the slope of the line that goes through the points and is m=-8%2F5


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=%28-8%2F5%29%28x-9%29 Plug in m=-8%2F5, x%5B1%5D=9, and y%5B1%5D=-2


y%2B2=%28-8%2F5%29%28x-9%29 Rewrite y--2 as y%2B2


y%2B2=%28-8%2F5%29x%2B%28-8%2F5%29%28-9%29 Distribute


y%2B2=%28-8%2F5%29x%2B72%2F5 Multiply


y=%28-8%2F5%29x%2B72%2F5-2 Subtract 2 from both sides.


y=%28-8%2F5%29x%2B62%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-8%2F5%29x%2B62%2F5