SOLUTION: Here is the question Write an equatio in standard form for a line that passes through each pair of points. 1.(3,1),(-1,-3) 2.(3,4),(-1,-4) thank you for your help!

Algebra ->  College  -> Linear Algebra -> SOLUTION: Here is the question Write an equatio in standard form for a line that passes through each pair of points. 1.(3,1),(-1,-3) 2.(3,4),(-1,-4) thank you for your help!      Log On


   

Question 146876: Here is the question
Write an equatio in standard form for a line that passes through each pair of points.
1.(3,1),(-1,-3)
2.(3,4),(-1,-4)
thank you for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

# 1



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=%28-3-1%29%2F%28-1-3%29 Plug in y%5B2%5D=-3, y%5B1%5D=1, x%5B2%5D=-1, x%5B1%5D=3, ,


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


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


m=1 Reduce


So the slope of the line that goes through the points and is m=1


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


y-1=1x%2B1%28-3%29 Distribute


y-1=1x-3 Multiply


y=1x-3%2B1 Add 1 to both sides.


y=1x-2 Combine like terms.


y=x-2 Simplify


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


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