SOLUTION: f(-2) = 2,f(0) = -4

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Question 375914: f(-2) = 2,f(0) = -4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since f(-2) = 2,f(0) = -4, we know that the line goes through the points (-2,0) and (0,-4)



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=-2 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=-4.


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


m=%28-4-0%29%2F%280--2%29 Plug in y%5B2%5D=-4, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2


m=%28-4%29%2F%280--2%29 Subtract 0 from -4 to get -4


m=%28-4%29%2F%282%29 Subtract -2 from 0 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-0=-2%28x--2%29 Plug in m=-2, x%5B1%5D=-2, and y%5B1%5D=0


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


y-0=-2x%2B-2%282%29 Distribute


y-0=-2x-4 Multiply


y=-2x-4 Simplify


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


So the function is f%28x%29=-2x-4


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

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Jim