SOLUTION: find the equation of the line that passes through the points (2,0)(4,6) not sure how to do this

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Question 281589: find the equation of the line that passes through the points (2,0)(4,6) not sure how to do this
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=0.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=6.


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


m=%286-0%29%2F%284-2%29 Plug in y%5B2%5D=6, y%5B1%5D=0, x%5B2%5D=4, and x%5B1%5D=2


m=%286%29%2F%284-2%29 Subtract 0 from 6 to get 6


m=%286%29%2F%282%29 Subtract 2 from 4 to get 2


m=3 Reduce


So the slope of the line that goes through the points and is m=3


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-0=3%28x-2%29 Plug in m=3, x%5B1%5D=2, and y%5B1%5D=0


y-0=3x%2B3%28-2%29 Distribute


y-0=3x-6 Multiply


y=3x-6 Simplify



So the equation that goes through the points and is y=3x-6


Notice how the graph of y=3x-6 goes through the points and . So this visually verifies our answer.
Graph of y=3x-6 through the points and