SOLUTION: Write an equation for the line containing points D and E D(-3, 6), E(-1,0)

Algebra ->  Linear-equations -> SOLUTION: Write an equation for the line containing points D and E D(-3, 6), E(-1,0)      Log On


   

Question 186940: Write an equation for the line containing points D and E
D(-3, 6), E(-1,0)
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 and is the second point .


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


m=%280-6%29%2F%28-1--3%29 Plug in y%5B2%5D=0, y%5B1%5D=6, x%5B2%5D=-1, and x%5B1%5D=-3


m=%28-6%29%2F%28-1--3%29 Subtract 6 from 0 to get -6


m=%28-6%29%2F%282%29 Subtract -3 from -1 to get 2


m=-3 Reduce


So the slope of the line that goes through the points and is m=-3


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-6=-3%28x--3%29 Plug in m=-3, x%5B1%5D=-3, and y%5B1%5D=6


y-6=-3%28x%2B3%29 Rewrite x--3 as x%2B3


y-6=-3x%2B-3%283%29 Distribute


y-6=-3x-9 Multiply


y=-3x-9%2B6 Add 6 to both sides.


y=-3x-3 Combine like terms.


y=-3x-3 Simplify


So the equation that goes through the points and is y=-3x-3


Notice how the graph of y=-3x-3 goes through the points and . So this visually verifies our answer.
Graph of y=-3x-3 through the points and