SOLUTION: (-4,2) and (2,4)I need to write the equation of each line passing through the given pair of points Please explain this Sandy new student

Algebra ->  Linear-equations -> SOLUTION: (-4,2) and (2,4)I need to write the equation of each line passing through the given pair of points Please explain this Sandy new student      Log On


   

Question 916712: (-4,2) and (2,4)I need to write the equation of each line passing through the given pair of points
Please explain this
Sandy new student
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=-4 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=2 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%282--4%29 Plug in y%5B2%5D=4, y%5B1%5D=2, x%5B2%5D=2, and x%5B1%5D=-4


m=%282%29%2F%282--4%29 Subtract 2 from 4 to get 2


m=%282%29%2F%286%29 Subtract -4 from 2 to get 6


m=1%2F3 Reduce


So the slope of the line that goes through the points and is m=1%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-2=%281%2F3%29%28x--4%29 Plug in m=1%2F3, x%5B1%5D=-4, and y%5B1%5D=2


y-2=%281%2F3%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-2=%281%2F3%29x%2B%281%2F3%29%284%29 Distribute


y-2=%281%2F3%29x%2B4%2F3 Multiply


y=%281%2F3%29x%2B4%2F3%2B2 Add 2 to both sides.


y=%281%2F3%29x%2B10%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=%281%2F3%29x%2B10%2F3

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim