SOLUTION: Find an equation for the line that passes through the points (5, -4) and (1, -2)

Algebra ->  Linear-equations -> SOLUTION: Find an equation for the line that passes through the points (5, -4) and (1, -2)      Log On


   

Question 321515: Find an equation for the line that passes through the points (5, -4) and (1, -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=5 and y%5B1%5D=-4.
Also, is the second point . So this means that x%5B2%5D=1 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--4%29%2F%281-5%29 Plug in y%5B2%5D=-2, y%5B1%5D=-4, x%5B2%5D=1, and x%5B1%5D=5


m=%282%29%2F%281-5%29 Subtract -4 from -2 to get 2


m=%282%29%2F%28-4%29 Subtract 5 from 1 to get -4


m=-1%2F2 Reduce


So the slope of the line that goes through the points and is m=-1%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--4=%28-1%2F2%29%28x-5%29 Plug in m=-1%2F2, x%5B1%5D=5, and y%5B1%5D=-4


y%2B4=%28-1%2F2%29%28x-5%29 Rewrite y--4 as y%2B4


y%2B4=%28-1%2F2%29x%2B%28-1%2F2%29%28-5%29 Distribute


y%2B4=%28-1%2F2%29x%2B5%2F2 Multiply


y=%28-1%2F2%29x%2B5%2F2-4 Subtract 4 from both sides.


y=%28-1%2F2%29x-3%2F2 Combine like terms.


So the equation that goes through the points and is y=%28-1%2F2%29x-3%2F2