SOLUTION: Write an equation for the line that passes through (2,1) and (3,5)

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Question 544699: Write an equation for the line that passes through (2,1) and (3,5)
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=2 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=5.


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


m=%285-1%29%2F%283-2%29 Plug in y%5B2%5D=5, y%5B1%5D=1, x%5B2%5D=3, and x%5B1%5D=2


m=%284%29%2F%283-2%29 Subtract 1 from 5 to get 4


m=%284%29%2F%281%29 Subtract 2 from 3 to get 1


m=4 Reduce


So the slope of the line that goes through the points and is m=4


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


y-1=4x%2B4%28-2%29 Distribute


y-1=4x-8 Multiply


y=4x-8%2B1 Add 1 to both sides.


y=4x-7 Combine like terms.


So the equation that goes through the points and is y=4x-7


Notice how the graph of y=4x-7 goes through the points and . So this visually verifies our answer.
Graph of y=4x-7 through the points and