SOLUTION: What is the equation of a line that passes through the points (0,2) and (4,4)?

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Question 205949: What is the equation of a line that passes through the points (0,2) and (4,4)?

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=0 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=4.


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


m=%284-2%29%2F%284-0%29 Plug in y%5B2%5D=4, y%5B1%5D=2, x%5B2%5D=4, and x%5B1%5D=0


m=%282%29%2F%284-0%29 Subtract 2 from 4 to get 2


m=%282%29%2F%284%29 Subtract 0 from 4 to get 4


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-2=%281%2F2%29%28x-0%29 Plug in m=1%2F2, x%5B1%5D=0, and y%5B1%5D=2


y-2=%281%2F2%29x%2B%281%2F2%29%28-0%29 Distribute


y-2=%281%2F2%29x%2B0 Multiply


y=%281%2F2%29x%2B0%2B2 Add 2 to both sides.


y=%281%2F2%29x%2B2 Combine like terms.


y=%281%2F2%29x%2B2 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B2


Notice how the graph of y=%281%2F2%29x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B2 through the points and