SOLUTION: Based on these two points, find the equation of the line connecting these two points. (7,8)(18,30)

Algebra ->  Linear-equations -> SOLUTION: Based on these two points, find the equation of the line connecting these two points. (7,8)(18,30)      Log On


   

Question 822918: Based on these two points, find the equation of the line connecting these two points. (7,8)(18,30)
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=7 and y%5B1%5D=8.
Also, is the second point . So this means that x%5B2%5D=18 and y%5B2%5D=30.


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


m=%2830-8%29%2F%2818-7%29 Plug in y%5B2%5D=30, y%5B1%5D=8, x%5B2%5D=18, and x%5B1%5D=7


m=%2822%29%2F%2818-7%29 Subtract 8 from 30 to get 22


m=%2822%29%2F%2811%29 Subtract 7 from 18 to get 11


m=2 Reduce


So the slope of the line that goes through the points and is m=2


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-8=2%28x-7%29 Plug in m=2, x%5B1%5D=7, and y%5B1%5D=8


y-8=2x%2B2%28-7%29 Distribute


y-8=2x-14 Multiply


y=2x-14%2B8 Add 8 to both sides.


y=2x-6 Combine like terms.


So the equation that goes through the points and is y=2x-6