SOLUTION: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).

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Question 549946: Find an equation in slope-intercept form passing through the points (2,5) and (7,-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=2 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=7 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=%28-3-5%29%2F%287-2%29 Plug in y%5B2%5D=-3, y%5B1%5D=5, x%5B2%5D=7, and x%5B1%5D=2


m=%28-8%29%2F%287-2%29 Subtract 5 from -3 to get -8


m=%28-8%29%2F%285%29 Subtract 2 from 7 to get 5


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


y-5=%28-8%2F5%29x%2B%28-8%2F5%29%28-2%29 Distribute


y-5=%28-8%2F5%29x%2B16%2F5 Multiply


y=%28-8%2F5%29x%2B16%2F5%2B5 Add 5 to both sides.


y=%28-8%2F5%29x%2B41%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%2B41%2F5