SOLUTION: i am working on linear equations for my test tomorrow, but I am stumped on one problem right now with these points M (3,6) and N (-3,-4)...what is the answer to y=mx+b for this

Algebra ->  Linear-equations -> SOLUTION: i am working on linear equations for my test tomorrow, but I am stumped on one problem right now with these points M (3,6) and N (-3,-4)...what is the answer to y=mx+b for this      Log On


   

Question 397150: i am working on linear equations for my test tomorrow, but I am stumped on one problem right now with these points M (3,6) and N (-3,-4)...what is the answer to y=mx+b for this
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=6.
Also, is the second point . So this means that x%5B2%5D=-3 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=%28-4-6%29%2F%28-3-3%29 Plug in y%5B2%5D=-4, y%5B1%5D=6, x%5B2%5D=-3, and x%5B1%5D=3


m=%28-10%29%2F%28-3-3%29 Subtract 6 from -4 to get -10


m=%28-10%29%2F%28-6%29 Subtract 3 from -3 to get -6


m=5%2F3 Reduce


So the slope of the line that goes through the points and is m=5%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-6=%285%2F3%29%28x-3%29 Plug in m=5%2F3, x%5B1%5D=3, and y%5B1%5D=6


y-6=%285%2F3%29x%2B%285%2F3%29%28-3%29 Distribute


y-6=%285%2F3%29x-5 Multiply


y=%285%2F3%29x-5%2B6 Add 6 to both sides.


y=%285%2F3%29x%2B1 Combine like terms.


So the equation that goes through the points and is y=%285%2F3%29x%2B1


Notice how the graph of y=%285%2F3%29x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=%285%2F3%29x%2B1 through the points and


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

Also, feel free to check out my tutoring website

Jim