SOLUTION: I don't understand Linear Equations. My teacher does the notes too fast in class and I can't keep up with the lesson and then I don't understand it. What I do not understand is how

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I don't understand Linear Equations. My teacher does the notes too fast in class and I can't keep up with the lesson and then I don't understand it. What I do not understand is how      Log On


   

Question 696675: I don't understand Linear Equations. My teacher does the notes too fast in class and I can't keep up with the lesson and then I don't understand it. What I do not understand is how you get the linear equation for two given points. How do you get the linear equation for "Write a linear equation for the line going through the points (-3, 105) and (6, -3"?


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=105.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=-3.


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


m=%28-3-105%29%2F%286--3%29 Plug in y%5B2%5D=-3, y%5B1%5D=105, x%5B2%5D=6, and x%5B1%5D=-3


m=%28-108%29%2F%286--3%29 Subtract 105 from -3 to get -108


m=%28-108%29%2F%289%29 Subtract -3 from 6 to get 9


m=-12 Reduce


So the slope of the line that goes through the points and is m=-12


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-105=-12%28x--3%29 Plug in m=-12, x%5B1%5D=-3, and y%5B1%5D=105


y-105=-12%28x%2B3%29 Rewrite x--3 as x%2B3


y-105=-12x%2B-12%283%29 Distribute


y-105=-12x-36 Multiply


y=-12x-36%2B105 Add 105 to both sides.


y=-12x%2B69 Combine like terms.


So the equation that goes through the points and is y=-12x%2B69