SOLUTION: Find an equation of the line containing the given pair of points. Express your answer in the form x=a, y=b, or y=mx+b, (-6,-6) and (5,5) what is an equation of the line? I'm having

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Find an equation of the line containing the given pair of points. Express your answer in the form x=a, y=b, or y=mx+b, (-6,-6) and (5,5) what is an equation of the line? I'm having      Log On


   

Question 236462: Find an equation of the line containing the given pair of points. Express your answer in the form x=a, y=b, or y=mx+b, (-6,-6) and (5,5) what is an equation of the line? I'm having a hard time understanding it, can you please help me slove and understand the equation??
Thank you! :))
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=-6 and y%5B1%5D=-6.
Also, is the second point . So this means that x%5B2%5D=5 and y%5B2%5D=5.


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


m=%285--6%29%2F%285--6%29 Plug in y%5B2%5D=5, y%5B1%5D=-6, x%5B2%5D=5, and x%5B1%5D=-6


m=%2811%29%2F%285--6%29 Subtract -6 from 5 to get 11


m=%2811%29%2F%2811%29 Subtract -6 from 5 to get 11


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--6=1%28x--6%29 Plug in m=1, x%5B1%5D=-6, and y%5B1%5D=-6


y--6=1%28x%2B6%29 Rewrite x--6 as x%2B6


y%2B6=1%28x%2B6%29 Rewrite y--6 as y%2B6


y%2B6=1x%2B1%286%29 Distribute


y%2B6=1x%2B6 Multiply


y=1x%2B6-6 Subtract 6 from both sides.


y=1x%2B0 Combine like terms.


y=1x Remove the trailing zero


y=x Simplify


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


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