SOLUTION: How do I find the equation of the line which passes through the points (-3,2) and (3,-2)

Algebra ->  Linear-equations -> SOLUTION: How do I find the equation of the line which passes through the points (-3,2) and (3,-2)      Log On


   

Question 212930: How do I find the equation of the line which passes through the points
(-3,2) 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=-3 and y%5B1%5D=2.
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=%28-2-2%29%2F%283--3%29 Plug in y%5B2%5D=-2, y%5B1%5D=2, x%5B2%5D=3, and x%5B1%5D=-3


m=%28-4%29%2F%283--3%29 Subtract 2 from -2 to get -4


m=%28-4%29%2F%286%29 Subtract -3 from 3 to get 6


m=-2%2F3 Reduce


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


y-2=%28-2%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-2=%28-2%2F3%29x%2B%28-2%2F3%29%283%29 Distribute


y-2=%28-2%2F3%29x-2 Multiply


y=%28-2%2F3%29x-2%2B2 Add 2 to both sides.


y=%28-2%2F3%29x%2B0 Combine like terms.


y=%28-2%2F3%29x Simplify


So the equation that goes through the points and is y=%28-2%2F3%29x


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