SOLUTION: Write an equation of the line that passes through the pair of points, (-3,-2),(5,4)

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Question 395379: Write an equation of the line that passes through the pair of points, (-3,-2),(5,4)
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=-3 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=5 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--2%29%2F%285--3%29 Plug in y%5B2%5D=4, y%5B1%5D=-2, x%5B2%5D=5, and x%5B1%5D=-3


m=%286%29%2F%285--3%29 Subtract -2 from 4 to get 6


m=%286%29%2F%288%29 Subtract -3 from 5 to get 8


m=3%2F4 Reduce


So the slope of the line that goes through the points and is m=3%2F4


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=%283%2F4%29%28x--3%29 Plug in m=3%2F4, x%5B1%5D=-3, and y%5B1%5D=-2


y--2=%283%2F4%29%28x%2B3%29 Rewrite x--3 as x%2B3


y%2B2=%283%2F4%29%28x%2B3%29 Rewrite y--2 as y%2B2


y%2B2=%283%2F4%29x%2B%283%2F4%29%283%29 Distribute


y%2B2=%283%2F4%29x%2B9%2F4 Multiply


y=%283%2F4%29x%2B9%2F4-2 Subtract 2 from both sides.


y=%283%2F4%29x%2B1%2F4 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=%283%2F4%29x%2B1%2F4


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim