SOLUTION: how can you write an equation of the line that connects points (-3,7) and (4,2)?

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Question 173255This question is from textbook
: how can you write an equation of the line that connects points (-3,7) and (4,2)?This question is from textbook

Answer by jim_thompson5910(21685) 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


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


m=%282-7%29%2F%284--3%29 Plug in y%5B2%5D=2, y%5B1%5D=7, x%5B2%5D=4, and x%5B1%5D=-3


m=%28-5%29%2F%284--3%29 Subtract 7 from 2 to get -5


m=%28-5%29%2F%287%29 Subtract -3 from 4 to get 7


So the slope of the line that goes through the points and is m=-5%2F7


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=%28-5%2F7%29%28x--3%29 Plug in m=-5%2F7, x%5B1%5D=-3, and y%5B1%5D=7


y-7=%28-5%2F7%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-7=%28-5%2F7%29x%2B%28-5%2F7%29%283%29 Distribute


y-7=%28-5%2F7%29x-15%2F7 Multiply


y=%28-5%2F7%29x-15%2F7%2B7 Add 7 to both sides.


y=%28-5%2F7%29x%2B34%2F7 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=%28-5%2F7%29x%2B34%2F7