SOLUTION: Find an equation of the line containing the points (1, -1) and (3, 2).

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line containing the points (1, -1) and (3, 2).      Log On


   

Question 847706: Find an equation of the line containing the points (1, -1) and (3, 2).
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=1 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=2.


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


m=%282--1%29%2F%283-1%29 Plug in y%5B2%5D=2, y%5B1%5D=-1, x%5B2%5D=3, and x%5B1%5D=1


m=%283%29%2F%283-1%29 Subtract -1 from 2 to get 3


m=%283%29%2F%282%29 Subtract 1 from 3 to get 2


So the slope of the line that goes through the points and is m=3%2F2


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=%283%2F2%29%28x-1%29 Plug in m=3%2F2, x%5B1%5D=1, and y%5B1%5D=-1


y%2B1=%283%2F2%29%28x-1%29 Rewrite y--1 as y%2B1


y%2B1=%283%2F2%29x%2B%283%2F2%29%28-1%29 Distribute


y%2B1=%283%2F2%29x-3%2F2 Multiply


y=%283%2F2%29x-3%2F2-1 Subtract 1 from both sides.


y=%283%2F2%29x-5%2F2 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=%283%2F2%29x-5%2F2