SOLUTION: write an equation for the line hrough the given point.(5,7),(6,8)

Algebra ->  Equations -> SOLUTION: write an equation for the line hrough the given point.(5,7),(6,8)      Log On


   

Question 595634: write an equation for the line hrough the given point.(5,7),(6,8)
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=5 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=8.


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


m=%288-7%29%2F%286-5%29 Plug in y%5B2%5D=8, y%5B1%5D=7, x%5B2%5D=6, and x%5B1%5D=5


m=%281%29%2F%286-5%29 Subtract 7 from 8 to get 1


m=%281%29%2F%281%29 Subtract 5 from 6 to get 1


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-7=1%28x-5%29 Plug in m=1, x%5B1%5D=5, and y%5B1%5D=7


y-7=1x%2B1%28-5%29 Distribute


y-7=1x-5 Multiply


y=1x-5%2B7 Add 7 to both sides.


y=1x%2B2 Combine like terms.


y=x%2B2 Simplify


So the equation that goes through the points and is y=x%2B2


Notice how the graph of y=x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=x%2B2 through the points and