SOLUTION: what is a line passing through the points (3,4) and (7,0)?

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Question 334544: what is a line passing through the points (3,4) and (7,0)?



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


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


m=%280-4%29%2F%287-3%29 Plug in y%5B2%5D=0, y%5B1%5D=4, x%5B2%5D=7, and x%5B1%5D=3


m=%28-4%29%2F%287-3%29 Subtract 4 from 0 to get -4


m=%28-4%29%2F%284%29 Subtract 3 from 7 to get 4


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-3%29 Plug in m=-1, x%5B1%5D=3, and y%5B1%5D=4


y-4=-1x%2B-1%28-3%29 Distribute


y-4=-1x%2B3 Multiply


y=-1x%2B3%2B4 Add 4 to both sides.


y=-1x%2B7 Combine like terms.


y=-x%2B7 Simplify


So the equation that goes through the points and is y=-x%2B7


Notice how the graph of y=-x%2B7 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B7 through the points and