SOLUTION: Find equation of each line in form of Y=MX+b The line thru 3,2 and orgin

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Question 145681: Find equation of each line in form of Y=MX+b
The line thru 3,2 and orgin
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, the "origin" is simply the point (0,0)




First let's find the slope 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=%280-2%29%2F%280-3%29 Plug in y%5B2%5D=0, y%5B1%5D=2, x%5B2%5D=0, x%5B1%5D=3, ,


m=%28-2%29%2F%280-3%29 Subtract 2 from 0 to get -2


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


m=2%2F3 Reduce


So the slope of the line that goes through the points and is m=2%2F3


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=%282%2F3%29%28x-3%29 Plug in m=2%2F3, x%5B1%5D=3, and y%5B1%5D=2


y-2=%282%2F3%29x%2B%282%2F3%29%28-3%29 Distribute


y-2=%282%2F3%29x-2 Multiply


y=%282%2F3%29x-2%2B2 Add 2 to both sides.


y=%282%2F3%29x%2B0 Combine like terms.


y=%282%2F3%29x Remove the trailing zero


So the equation that goes through the points and is y=%282%2F3%29x


Notice how the graph of y=%282%2F3%29x goes through the points and . So this visually verifies our answer.
Graph of y=%282%2F3%29x through the points and