SOLUTION: Please help me solve this: Write the equation of the graph passing through the points (-4,5) and (-2,3).

Algebra ->  Linear-equations -> SOLUTION: Please help me solve this: Write the equation of the graph passing through the points (-4,5) and (-2,3).      Log On


   

Question 545007: Please help me solve this: Write the equation of the graph passing through the points (-4,5) and (-2,3).
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=-4 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=3.


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


m=%283-5%29%2F%28-2--4%29 Plug in y%5B2%5D=3, y%5B1%5D=5, x%5B2%5D=-2, and x%5B1%5D=-4


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


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


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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-5=-1%28x--4%29 Plug in m=-1, x%5B1%5D=-4, and y%5B1%5D=5


y-5=-1%28x%2B4%29 Rewrite x--4 as x%2B4


y-5=-1x%2B-1%284%29 Distribute


y-5=-1x-4 Multiply


y=-1x-4%2B5 Add 5 to both sides.


y=-1x%2B1 Combine like terms.


y=-x%2B1 Simplify


So the equation that goes through the points and is y=-x%2B1


Notice how the graph of y=-x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B1 through the points and


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Jim