SOLUTION: Help with equations please? I need to find the equation of the lines joining the pairs of points: (2, 40) (4, 50) Any help appreciated! Thanks

Algebra ->  Coordinate-system -> SOLUTION: Help with equations please? I need to find the equation of the lines joining the pairs of points: (2, 40) (4, 50) Any help appreciated! Thanks      Log On


   

Question 469294: Help with equations please?
I need to find the equation of the lines joining the pairs of points:
(2, 40)
(4, 50)
Any help appreciated!
Thanks
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=2 and y%5B1%5D=40.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=50.


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


m=%2850-40%29%2F%284-2%29 Plug in y%5B2%5D=50, y%5B1%5D=40, x%5B2%5D=4, and x%5B1%5D=2


m=%2810%29%2F%284-2%29 Subtract 40 from 50 to get 10


m=%2810%29%2F%282%29 Subtract 2 from 4 to get 2


m=5 Reduce


So the slope of the line that goes through the points and is m=5


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-40=5%28x-2%29 Plug in m=5, x%5B1%5D=2, and y%5B1%5D=40


y-40=5x%2B5%28-2%29 Distribute


y-40=5x-10 Multiply


y=5x-10%2B40 Add 40 to both sides.


y=5x%2B30 Combine like terms.


So the equation that goes through the points and is y=5x%2B30