SOLUTION: what is the equation of a line that contains the points (1,1) and (3, 9)

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Question 537288: what is the equation of a line that contains the points (1,1) and (3, 9)
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=1 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=9.


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


m=%289-1%29%2F%283-1%29 Plug in y%5B2%5D=9, y%5B1%5D=1, x%5B2%5D=3, and x%5B1%5D=1


m=%288%29%2F%283-1%29 Subtract 1 from 9 to get 8


m=%288%29%2F%282%29 Subtract 1 from 3 to get 2


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


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


y-1=4x-4 Multiply


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


y=4x-3 Combine like terms.


y=4x-3 Simplify


So the equation that goes through the points and is y=4x-3


Notice how the graph of y=4x-3 goes through the points and . So this visually verifies our answer.
Graph of y=4x-3 through the points and


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Jim