SOLUTION: 4)Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible. Through (6,4) and (4,6) (simplify your answer.)

Algebra ->  Linear-equations -> SOLUTION: 4)Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible. Through (6,4) and (4,6) (simplify your answer.)      Log On


   

Question 382114: 4)Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible.
Through (6,4) and (4,6)
(simplify your answer.)
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=4.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=6.


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


m=%286-4%29%2F%284-6%29 Plug in y%5B2%5D=6, y%5B1%5D=4, x%5B2%5D=4, and x%5B1%5D=6


m=%282%29%2F%284-6%29 Subtract 4 from 6 to get 2


m=%282%29%2F%28-2%29 Subtract 6 from 4 to get -2


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-4=-1%28x-6%29 Plug in m=-1, x%5B1%5D=6, and y%5B1%5D=4


y-4=-1x%2B-1%28-6%29 Distribute


y-4=-1x%2B6 Multiply


y=-1x%2B6%2B4 Add 4 to both sides.


y=-1x%2B10 Combine like terms.


y=-x%2B10 Simplify


So the equation that goes through the points and is y=-x%2B10


Notice how the graph of y=-x%2B10 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B10 through the points and


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim