SOLUTION: write the equation of the line passing through the points (5,-2) and (9,-2)

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Question 750885: write the equation of the line passing through the points (5,-2) and (9,-2)
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=5 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=9 and y%5B2%5D=-2.


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


m=%28-2--2%29%2F%289-5%29 Plug in y%5B2%5D=-2, y%5B1%5D=-2, x%5B2%5D=9, and x%5B1%5D=5


m=%280%29%2F%289-5%29 Subtract -2 from -2 to get 0


m=%280%29%2F%284%29 Subtract 5 from 9 to get 4


m=0 Reduce


So the slope of the line that goes through the points and is m=0


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


y%2B2=0%28x-5%29 Rewrite y--2 as y%2B2


y%2B2=0x%2B0%28-5%29 Distribute


y%2B2=0x%2B0 Multiply


y=0x%2B0-2 Subtract 2 from both sides.


y=0x-2 Combine like terms.


y=-2 Simplify


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


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