SOLUTION: My problem is Find the equation of the line that contains the point (-2,3)(4,2). I'm pretty sure this is a simple problem..I've just forgotten where to start. Help would be greatl

Algebra ->  Graphs -> SOLUTION: My problem is Find the equation of the line that contains the point (-2,3)(4,2). I'm pretty sure this is a simple problem..I've just forgotten where to start. Help would be greatl      Log On


   

Question 152519: My problem is Find the equation of the line that contains the point (-2,3)(4,2).
I'm pretty sure this is a simple problem..I've just forgotten where to start. Help would be greatly appreciated. Thanks.
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


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


m=%282-3%29%2F%284--2%29 Plug in y%5B2%5D=2, y%5B1%5D=3, x%5B2%5D=4, x%5B1%5D=-2, ,


m=%28-1%29%2F%284--2%29 Subtract 3 from 2 to get -1


m=%28-1%29%2F%286%29 Subtract -2 from 4 to get 6


So the slope of the line that goes through the points and is m=-1%2F6


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-3=%28-1%2F6%29%28x--2%29 Plug in m=-1%2F6, x%5B1%5D=-2, and y%5B1%5D=3


y-3=%28-1%2F6%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=%28-1%2F6%29x%2B%28-1%2F6%29%282%29 Distribute


y-3=%28-1%2F6%29x-1%2F3 Multiply


y=%28-1%2F6%29x-1%2F3%2B3 Add 3 to both sides.


y=%28-1%2F6%29x%2B8%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=%28-1%2F6%29x%2B8%2F3


Notice how the graph of y=%28-1%2F6%29x%2B8%2F3 goes through the points and . So this visually verifies our answer.
Graph of y=%28-1%2F6%29x%2B8%2F3 through the points and