SOLUTION: write the equation of the line though (5,-2) and (2,10)

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Question 550327: write the equation of the line though (5,-2) and (2,10)
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=2 and y%5B2%5D=10.


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


m=%2810--2%29%2F%282-5%29 Plug in y%5B2%5D=10, y%5B1%5D=-2, x%5B2%5D=2, and x%5B1%5D=5


m=%2812%29%2F%282-5%29 Subtract -2 from 10 to get 12


m=%2812%29%2F%28-3%29 Subtract 5 from 2 to get -3


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--2=-4%28x-5%29 Plug in m=-4, x%5B1%5D=5, and y%5B1%5D=-2


y%2B2=-4%28x-5%29 Rewrite y--2 as y%2B2


y%2B2=-4x%2B-4%28-5%29 Distribute


y%2B2=-4x%2B20 Multiply


y=-4x%2B20-2 Subtract 2 from both sides.


y=-4x%2B18 Combine like terms.


So the equation that goes through the points and is y=-4x%2B18


Notice how the graph of y=-4x%2B18 goes through the points and . So this visually verifies our answer.
Graph of y=-4x%2B18 through the points and