SOLUTION: find the equation of the line that passes through the points (3,7) and (-4,0).

Algebra ->  Linear-equations -> SOLUTION: find the equation of the line that passes through the points (3,7) and (-4,0).      Log On


   

Question 179006: find the equation of the line that passes through the points (3,7) and (-4,0).
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 and is the second point .


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


m=%280-7%29%2F%28-4-3%29 Plug in y%5B2%5D=0, y%5B1%5D=7, x%5B2%5D=-4, and x%5B1%5D=3


m=%28-7%29%2F%28-4-3%29 Subtract 7 from 0 to get -7


m=%28-7%29%2F%28-7%29 Subtract 3 from -4 to get -7


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-3%29 Plug in m=1, x%5B1%5D=3, and y%5B1%5D=7


y-7=1x%2B1%28-3%29 Distribute


y-7=1x-3 Multiply


y=1x-3%2B7 Add 7 to both sides.


y=1x%2B4 Combine like terms.


y=x%2B4 Simplify


So the equation that goes through the points and is y=x%2B4


Notice how the graph of y=x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=x%2B4 through the points and