SOLUTION: Find an equation given of the line containing these two points (4,3)(12,7)

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Question 149950: Find an equation given of the line containing these two points (4,3)(12,7)
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=%287-3%29%2F%2812-4%29 Plug in y%5B2%5D=7, y%5B1%5D=3, x%5B2%5D=12, x%5B1%5D=4, ,


m=%284%29%2F%2812-4%29 Subtract 3 from 7 to get 4


m=%284%29%2F%288%29 Subtract 4 from 12 to get 8


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%2F2


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-3=%281%2F2%29%28x-4%29 Plug in m=1%2F2, x%5B1%5D=4, and y%5B1%5D=3


y-3=%281%2F2%29x%2B%281%2F2%29%28-4%29 Distribute


y-3=%281%2F2%29x-2 Multiply


y=%281%2F2%29x-2%2B3 Add 3 to both sides.


y=%281%2F2%29x%2B1 Combine like terms.


y=%281%2F2%29x%2B1 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B1


Notice how the graph of y=%281%2F2%29x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B1 through the points and