SOLUTION: write the equation of the line that passes through the following points (5, -3),(8,4)

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Question 293607: write the equation of the line that passes through the following points (5, -3),(8,4)
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=-3.
Also, is the second point . So this means that x%5B2%5D=8 and y%5B2%5D=4.


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


m=%284--3%29%2F%288-5%29 Plug in y%5B2%5D=4, y%5B1%5D=-3, x%5B2%5D=8, and x%5B1%5D=5


m=%287%29%2F%288-5%29 Subtract -3 from 4 to get 7


m=%287%29%2F%283%29 Subtract 5 from 8 to get 3


So the slope of the line that goes through the points and is m=7%2F3


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--3=%287%2F3%29%28x-5%29 Plug in m=7%2F3, x%5B1%5D=5, and y%5B1%5D=-3


y%2B3=%287%2F3%29%28x-5%29 Rewrite y--3 as y%2B3


y%2B3=%287%2F3%29x%2B%287%2F3%29%28-5%29 Distribute


y%2B3=%287%2F3%29x-35%2F3 Multiply


y=%287%2F3%29x-35%2F3-3 Subtract 3 from both sides.


y=%287%2F3%29x-44%2F3 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=%287%2F3%29x-44%2F3