SOLUTION: what is an equation of a line that passes through points (5,4) and (-2,0)

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Question 585488: what is an equation of a line that passes through points (5,4) and (-2,0)
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=4.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=0.


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


m=%280-4%29%2F%28-2-5%29 Plug in y%5B2%5D=0, y%5B1%5D=4, x%5B2%5D=-2, and x%5B1%5D=5


m=%28-4%29%2F%28-2-5%29 Subtract 4 from 0 to get -4


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


m=4%2F7 Reduce


So the slope of the line that goes through the points and is m=4%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-4=%284%2F7%29%28x-5%29 Plug in m=4%2F7, x%5B1%5D=5, and y%5B1%5D=4


y-4=%284%2F7%29x%2B%284%2F7%29%28-5%29 Distribute


y-4=%284%2F7%29x-20%2F7 Multiply


y=%284%2F7%29x-20%2F7%2B4 Add 4 to both sides.


y=%284%2F7%29x%2B8%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=%284%2F7%29x%2B8%2F7

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