SOLUTION: Which is an equation for the line that contains the points (-3, 5) and (1, -3)?

Algebra ->  Linear-equations -> SOLUTION: Which is an equation for the line that contains the points (-3, 5) and (1, -3)?      Log On


   

Question 612948: Which is an equation for the line that contains the points (-3, 5) and (1, -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=5.
Also, is the second point . So this means that x%5B2%5D=1 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=%28-3-5%29%2F%281--3%29 Plug in y%5B2%5D=-3, y%5B1%5D=5, x%5B2%5D=1, and x%5B1%5D=-3


m=%28-8%29%2F%281--3%29 Subtract 5 from -3 to get -8


m=%28-8%29%2F%284%29 Subtract -3 from 1 to get 4


m=-2 Reduce


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


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


y-5=-2%28x%2B3%29 Rewrite x--3 as x%2B3


y-5=-2x%2B-2%283%29 Distribute


y-5=-2x-6 Multiply


y=-2x-6%2B5 Add 5 to both sides.


y=-2x-1 Combine like terms.


So the equation that goes through the points and is y=-2x-1


Notice how the graph of y=-2x-1 goes through the points and . So this visually verifies our answer.
Graph of y=-2x-1 through the points and