SOLUTION: 9. Find the equation of the line that goes through the points (-4,1) and (-1,4)

Algebra ->  Linear-equations -> SOLUTION: 9. Find the equation of the line that goes through the points (-4,1) and (-1,4)      Log On


   

Question 604762: 9. Find the equation of the line that goes through the points (-4,1) and (-1,4)
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=-4 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=4.


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


m=%284-1%29%2F%28-1--4%29 Plug in y%5B2%5D=4, y%5B1%5D=1, x%5B2%5D=-1, and x%5B1%5D=-4


m=%283%29%2F%28-1--4%29 Subtract 1 from 4 to get 3


m=%283%29%2F%283%29 Subtract -4 from -1 to get 3


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--4%29 Plug in m=1, x%5B1%5D=-4, and y%5B1%5D=1


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


y-1=1x%2B1%284%29 Distribute


y-1=1x%2B4 Multiply


y=1x%2B4%2B1 Add 1 to both sides.


y=1x%2B5 Combine like terms.


y=x%2B5 Simplify


So the equation that goes through the points and is y=x%2B5


Notice how the graph of y=x%2B5 goes through the points and . So this visually verifies our answer.
Graph of y=x%2B5 through the points and