SOLUTION: what is the equation,slope,and y-intercept for (3,9) and (5,5)?

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Question 555823: what is the equation,slope,and y-intercept for (3,9) and (5,5)?
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=3 and y%5B1%5D=9.
Also, is the second point . So this means that x%5B2%5D=5 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=%285-9%29%2F%285-3%29 Plug in y%5B2%5D=5, y%5B1%5D=9, x%5B2%5D=5, and x%5B1%5D=3


m=%28-4%29%2F%285-3%29 Subtract 9 from 5 to get -4


m=%28-4%29%2F%282%29 Subtract 3 from 5 to get 2


m=-2 Reduce


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


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-9=-2%28x-3%29 Plug in m=-2, x%5B1%5D=3, and y%5B1%5D=9


y-9=-2x%2B-2%28-3%29 Distribute


y-9=-2x%2B6 Multiply


y=-2x%2B6%2B9 Add 9 to both sides.


y=-2x%2B15 Combine like terms.


y=-2x%2B15 Simplify


So the equation that goes through the points and is y=-2x%2B15


Notice how the graph of y=-2x%2B15 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B15 through the points and

Note: this graph has a slope of -2 and a y-intercept of (0, 15)

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Jim