SOLUTION: How do I use the Two Point Formula to find the equation of the line joining the following pairs of points?: 1. (1,8) and (-1,-20) 2. (2,-1) and (3,5) I have a test on thes

Algebra ->  Linear-equations -> SOLUTION: How do I use the Two Point Formula to find the equation of the line joining the following pairs of points?: 1. (1,8) and (-1,-20) 2. (2,-1) and (3,5) I have a test on thes      Log On


   

Question 403332: How do I use the Two Point Formula to find the equation of the line joining the following pairs of points?:
1. (1,8) and (-1,-20)
2. (2,-1) and (3,5)
I have a test on these (coordinate geometry) tomorrow and I am still really confused on these. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



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=%28-20-8%29%2F%28-1-1%29 Plug in y%5B2%5D=-20, y%5B1%5D=8, x%5B2%5D=-1, and x%5B1%5D=1


m=%28-28%29%2F%28-1-1%29 Subtract 8 from -20 to get -28


m=%28-28%29%2F%28-2%29 Subtract 1 from -1 to get -2


m=14 Reduce


So the slope of the line that goes through the points and is m=14


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-8=14%28x-1%29 Plug in m=14, x%5B1%5D=1, and y%5B1%5D=8


y-8=14x%2B14%28-1%29 Distribute


y-8=14x-14 Multiply


y=14x-14%2B8 Add 8 to both sides.


y=14x-6 Combine like terms.



So the equation that goes through the points and is y=14x-6


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# 2



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=%285--1%29%2F%283-2%29 Plug in y%5B2%5D=5, y%5B1%5D=-1, x%5B2%5D=3, and x%5B1%5D=2


m=%286%29%2F%283-2%29 Subtract -1 from 5 to get 6


m=%286%29%2F%281%29 Subtract 2 from 3 to get 1


m=6 Reduce


So the slope of the line that goes through the points and is m=6


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--1=6%28x-2%29 Plug in m=6, x%5B1%5D=2, and y%5B1%5D=-1


y%2B1=6%28x-2%29 Rewrite y--1 as y%2B1


y%2B1=6x%2B6%28-2%29 Distribute


y%2B1=6x-12 Multiply


y=6x-12-1 Subtract 1 from both sides.


y=6x-13 Combine like terms.


So the equation that goes through the points and is y=6x-13