SOLUTION: Find an equation of the line containing the given pair of points. (1,2) and (3,3)

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Question 190109: Find an equation of the line containing the given pair of points.
(1,2) and (3,3)
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=%283-2%29%2F%283-1%29 Plug in y%5B2%5D=3, y%5B1%5D=2, x%5B2%5D=3, and x%5B1%5D=1


m=%281%29%2F%283-1%29 Subtract 2 from 3 to get 1


m=%281%29%2F%282%29 Subtract 1 from 3 to get 2


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


y-2=%281%2F2%29x%2B%281%2F2%29%28-1%29 Distribute


y-2=%281%2F2%29x-1%2F2 Multiply


y=%281%2F2%29x-1%2F2%2B2 Add 2 to both sides.


y=%281%2F2%29x%2B3%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


y=%281%2F2%29x%2B3%2F2 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B3%2F2


Notice how the graph of y=%281%2F2%29x%2B3%2F2 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B3%2F2 through the points and